THE TOP DOWN (AND MATHEMATICAL) UNIFICATION OF PHYSICS/PHYSICAL EXPERIENCE IS PROVEN: F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational (IN BALANCE). Therefore, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. In other words, gravitational force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (BALANCE AND completeness go hand in hand.) Consider what is THE SUN, and consider what is c (A POINT, A PHOTON). Now, consider our direct experience of what is NECESSARILY the BALANCED MIDDLE DISTANCE in/of SPACE. Perfect. Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. BALANCED inertia/INERTIAL RESISTANCE is fundamental, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The rotation of THE MOON MATCHES it's revolution, AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. This demonstrates the BALANCED EXTENSIVENESS of the MIDDLE DISTANCE in/of SPACE as NECESSARILY and FUNDAMENTALLY electromagnetic/gravitational (IN BALANCE). GREAT !!! Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. THE SUN (including the ORANGE SUN) AND THE EARTH (including the GROUND) are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma. Objects fall at the same rate, AS the SPEED OF LIGHT is RELATIVELY CONSTANT AS WELL. GREAT !!! It ALL makes perfect sense. The stars AND PLANETS are POINTS in the night sky. F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The balance of being AND EXPERIENCE is ESSENTIAL. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Indeed, the ability of THOUGHT to DESCRIBE OR RECONFIGURE sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience. THOUGHTS ARE INVISIBLE. Magnificent !!! THE SELF represents, FORMS, and experiences a COMPREHENSIVE approximation of experience in general by combining conscious and unconscious experience. THE EYE IS THE BODY, AND the DOME of a person's EYE is ALSO VISIBLE. BALANCE AND completeness go hand in hand. Indeed, the INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. Really THINK about it all. A PHOTON may be placed at the center of THE SUN (as A POINT, of course), as the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED. "Mass"/ENERGY are linked AND BALANCED. OVERLAY what is THE EYE in BALANCED RELATION to/WITH what is THE EARTH. NOW, LOOK at what is the semi-spherical, translucent, QUANTUM GRAVITATIONAL, AND BLUE SKY. The DOME of a person's EYE is ALSO VISIBLE. GREAT !!! THE EARTH is ALSO BLUE. Excellent !!! (Consider the black space of what is THE EYE as well, of course.) The ultimate unification (AND UNDERSTANDING) of physics/physical experience combines, BALANCES, and includes opposites. BALANCE AND completeness go hand in hand. Really THINK about it ALL. Great !!! There is no outsmarting the GENIUS of dreams. Dream experience is/involves true/real QUANTUM GRAVITY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Very importantly, outer "space" involves full inertia, AND it is fully invisible AND black. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. ACCORDINGLY, a given PLANET (INCLUDING WHAT IS THE EARTH) sweeps out equal areas in equal times; AND this is THEN consistent with/as F=ma, E=mc2, AND what is PERPETUAL MOTION; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. INDEED, GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. IT IS PROVEN. GREAT !!! ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. By Frank DiMeglio
Frank DiMeglio why is the fact that Earth’s moon is tidally locked with Earth’s rotation relevant to anything relating to electromagnetism *or* gravity? It’s just something that happens to be true at this moment in time, it wasn’t always true in the past and won’t continue to be so in the future. Also, your erratic and confusing use of ALL CAPS makes your writing exceedingly difficult to decipher; true genius knows how to communicate ideas effectively.
Dr. Hossenfelder, I was great at working out Differential Equations in my youth (I'm now 78). I stumbled on your video and decided to see if I have enough brain left to follow it through. I do, thank you. I love your passion of math and science, I have never lost my own. I look forward to whatever else you can reawaken in me.
I struggled so much last semester attempting to understand why we were solving these differential equations and what the outcomes meant. I was often told "If you see this, do this and you'll do fine." But "Why!!?" Thank you Dr. Hossenfelder, it fills me with joy, I finally understand why. *Opens differential equations textbook*
@@paulcarson7860 You exactly describe my personal experience 55 years ago. Never given any background, context or purpose for differential equations, but was taught to go through the motions. One of the greatest disappointments of my education. Thank you, Sabine.
@@unthawedwater747 The lack of "why" is often because you need to learn the subject material first before you can really explore the understanding of "the why" and, as a student, it is kinda your responsibility to figure out why you are doing things.
I used to ask questions, but everybody including professors were busy in preparing you for the "exam" and getting more marks in exam rather than the actual meaning behind these Mathematical concepts
@@Mastermindyoung14 it was hard back then, pre Internet era, you had to read multiple books and also learn other subjects. If we have to do everything, why do you need teachers with specialized fields then?
I took several courses in differential equations, many decades ago and I really enjoyed using them to model various behaviours. Partial differential equations and even stochastic differential equations I found even more interesting. I have forgotten almost all of that stuff in the time since.
Many people don’t know when buying shocks for their cars in reality they buying just the dumping coefficient of solution of a differential equation of an oscillating system created by car weight, spring and a hole in the ground.
That is the fastest summary of the use of differential equations I have ever encountered. How did you do it all in one breath? It is also the most concise and cogent explication of the fact that differential and partial differential equations are not esoteric but powerful tools for everyday use. Thank you Sabina. I shall make an offering at your shrine.
There is no meaning in life of speculative physicists ... that's why differential equations... If there were, the equations would called the equality equations...lol
@@shoopinc The physicists think they have the panacea and the jouvence spring together, any other idea or concept is crackpot or superstition. _That_ is rude.
I've been subscribed to Sabine for just over a year now an she's definitely the most charismatic science popularisers. When is she getting her own PBS or Netflix spot? I'm ready for it.
@@fesimco4339 All the stuff Dr Hossenfelder talks about where scientists are touting questionable science is propagated by mainstream media. If it’s on mainstream media, it’s not trustworthy.
@@fesimco4339 Not really. “Trust” means you don’t question it. I don’t believe any of it anymore. Is gravity a byproduct of the warping of “space-time” or an interaction with Higgs? Both are presented as “fact.”
I am mathematically impaired. I am incapable of grasping even the most basic mathematical concepts. I can understand everything in videos of this type up to and until the program starts to produce the mathematical reasoning behind every event in science. My grasp of numbers stopped at simple arithmetic. I wish it wasn't so, but at 81 I'm too old and set in my ways for anything to change me now. But, I do comprehend everything she is trying to explain. Sabine is a great explainer in a renowned history of great explainers.
so, you don't understand basic math but was able to understand DIFFERENTIAL EQUATIONS from a 10-minute video ? You are the same age and at the same "reasoning dexterity" as Biden 👍
If you like that particular exposition, you might also like her exposition of how the what is called "multiverse" fantasy is pure undiluted religion, which of course it is
If I hadn’t essentially failed Algebra 1 twice back in high school, I’m sure I’d enjoy your videos even more. Your presentations are the best, and I feel smarter for having watched them. 🧬🧪👩🔬
For the sake of some readers, I will mention that you might even say that the word "initial" in "initial conditions" refers to things you know at the start of solving the problem. You can also call initial conditions "boundary conditions" or "constraints", which simply tell you some extra information about the system, and these help you pick which one of the many possible solutions best fits the particular case you are considering.
“Boundary conditions” is a good general term, because you might be solving the equations under a variety of scenarios. For example, instead of starting at an initial time and extrapolating forwards, you might have observations at a given time (e.g. the present) and are trying to extrapolate backwards into the past. “Boundary” is a more general term than “initial” or “final”. And yes, it can also include spatial boundaries as well.
YES! Initial conditions, like weather conditions (or a double pendulum for a simple system) have feedback loops between multiple variables, and small errors in initial conditions completely dominate outcomes after some period of time.
Perhaps it should be also emphasized that, contrary to what a student may be lead to think from the calculus experience of solving explicitly differential equations via a bunch of tricks, *in real life science one rarely solves a differential equation* in that sense. In fact, it is feasible to find explicit solutions only for very restricted classes of such equations. Even in the very theory of (ordinary or partial) differential equations in Mathematical Analysis, one is almost never able to find explicit solutions, and finding the latter is not the goal anyway: the goal is to understand the properties of the solutions (individually or of the whole space they form). And even in the case in which it is possible to "write down" a solution (say by expressing it via a Fourier expansion), the expression is seldom useful in order to understand its properties. As for applied mathematics and physics, again, one typically doesn't solve DEs explicitely (physicists say "analytically"). Methods of numerical analysis are used instead, that allow one to get a numerical approximation (typically by using an extremely powerful computer).
Those words should be printed in BOLD FACE type on the first page of every textbook on ordinary differential equations. The "tricks" are neat, but the real solution is had by grinding it out numerically.
@@markotrieste I was just thinking that and you beat me to it. It’s about projecting, not predicting, and differential equations are used every second in infectious disease modelling
Had to scroll down pretty far to find your comment. Engineering students take 3 years of calculus and one year of DiffEq when they get their first job where they have to do something in the real world, they quickly discover the real world is not linear, it is partly chaotic, it is somewhat random, and the initial conditions are extremely difficult to define what you end up with from those 4 years of math is at BEST an approximation, never an exact 'correct' answer its demoralizing for engineers to discover after they believed they would be able to control everything with carefully designed systems what you end up with is a career steeped in probability and statistics
Interestingly enough, this topic hit me on the head when I started my first upper-division class in Physics at UCLA in 1968. I had taken all of the required math classes, such as calculus and so forth, for a Physics Major and I went into my first day of MECHANICS 101, the baseline Physics class for essentially everything else in my Physics Major to get my Bachelor Degree. I sit down and the class starts. The professor puts the HAMILTONIAN Differential Equation on the blackboard, one of the fundamental formulae for solving a LOT of Physics problems and absolutely essential to understand for this and all later Physics classes. A small problem, though: I had not taken ANY differential equations classes because they were not on the required list! I said to the professor: "That is a differential equation. I have not had any classes on how to solve them." He looked at me and said, with no exaggeration, "Then you had better learn fast!" I was so angry that I stomped all the way to the secretary of the Director of the Physics Department of UCLA (now combined with Astronomy) and stated that they have to change their requirements to warn students that they need to take Differential Equations BEFORE getting into upper-division classes. She said she would talk to the Director about this and I left. I do not know if it ever happened, though. What did happen for me was taking two classes in this end-to-end by the best professor I ever had, Dr. David Sanchez, and deciding to take a few more math classes to get a double bachelor degree in Math and Physics, so it did have a good result in the end. But I still get mad when I think about it...
Sabine is a gift to us thinking people. I have enjoyed many of her short physics videos, and now this one really brings those ancient studies back to life with new vision. Thank you so much.
I like the way she says certain words. So far, my favorite is "iron.' She pronounces the German ones correctly, too, like "Einstein," with the "sh" sound.
I know I am subscribed to a high quality content creator when I search something on TH-cam and among the top search results is a video from a channel I'm already subscribed to. My only regret is that I didn't find this channel sooner.
@@tillabakos2248 what I'm trying to tell is that is that what you commented is true. BUT comparing a teacher with Kardashian is an insult to the teacher. (Hope u get my point)
Not true. Endless numbers of people good at calculus have no clue how "nature" works. And the results of man calculations hold little insight into the mechanisms behind the numbers. The ability to do a calculation is not equivalent to understanding a thing.
It kills me that I could have learned calculus, *should* have but I didn't believe in my own intelligence and was trapped in a religion that discouraged higher learning. It would have greatly added to my other interests in physics, astronomy and now, evolution.
@@johnsmith1474 Sure, and despite the fact that I own a hammer and nails and have a whole bunch of wood, don't expect me to be doing any decent carpentry anytime soon. Just because someone has a tool, does not mean they can use it effectively. Calculus is a necessary (but not sufficient) tool for understanding how nature works. And this cannot be stressed enough: calculus (and maths in general) is *faaaar* more than than doing calculations. In 2020, an era where mankind is drowning in transistors, numerical calculation is probably the least useful thing an understanding of maths gives you.
@@johnsmith1474 he said it is a necessary tool to have, not that having it gives you the understanding it can be employed to achieve. And, of course, you need other tools, but he didn't say you don't... one really has to wonder what made you so determined to conflate opposite-moving logics like that
I have much suffered in grade 12 with these differential equations. The examples you gave did refresh my memory somehow and I wish I had had this kind of expose at the time. Well done!
Before watching this I wasn't sure what Differential Equations were. I still don't know but I love watching Sabine. I will have to watch this a few more times. Thanks Sabine.
So far I had differential equations in nuclear physics/radioactivity, on ossications/waves and in classical mechanics newtons laws. But I've also seen them in the navier stokes equations and einsteins general theory of relativity, as well as in the schrödinger equations. They are literally everywhere when you study physics, and they are the branch of maths I love the most.
Great video about "Diffe Qs". One of the things I remember when I took the course is that many differential equations cannot be solved using analysis. Please do a video on this. I have been viewing many of your videos and it's obvious you are an accomplished Theoretical Physicist with talent to teacher. That's why I ask.
Differential equations, linear algebra, probability/statistics, and number theory--four pillars for describing and understanding so much of what we see around us.
In addition to being informative and educational, your videos are always a fun watch due to the subtle humour sprinkled in here and there. Your channel is easily one of my favourites on TH-cam!
Is she not explaining how it is possible to calculate how mutually dependent causes and effects change? I simply switched off my associative apparatus when various bullies were trying to force me to learn what is called mathematics, but if they had explained to me or what differential equations might be useful, I might not have dismissed the entire subject as having no relevance or importance to me whatsoever - which as it has turned out, has been the case. I have never needed any kind of equation in my entire life or mathematics for that matter. I was forced to learn about differential equations and of course simply flat out refused to do so, because I could not see the point of them, or mathematics generally
I just realized how the way math was taught in school had completelly turned me off of exploring it, and only made me feel inadequate and stupid. It was a humiliating experience that caused me to ignore the topic for 40 years. I wasn't even trying, even though I knew I should be able to understand at least the basics. Now I'm finally learning the basics. This would have been easy - thanks for making so much knowledge accessible. I really like your calm style.
0:56 "To get an idea for how differential equations work, let us look at a simple example: The spread of a disease though the population". Fast forward to 01:46, after the "simple explanation"... and my brain is swimming. Thanks for keeping it so simple. 😵💫😵💫😵💫
THE TOP DOWN (AND MATHEMATICAL) UNIFICATION OF PHYSICS/PHYSICAL EXPERIENCE IS PROVEN: F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational (IN BALANCE). Therefore, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. In other words, gravitational force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (BALANCE AND completeness go hand in hand.) Consider what is THE SUN, and consider what is c (A POINT, A PHOTON). Now, consider our direct experience of what is NECESSARILY the BALANCED MIDDLE DISTANCE in/of SPACE. Perfect. Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE. BALANCED inertia/INERTIAL RESISTANCE is fundamental, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The rotation of THE MOON MATCHES it's revolution, AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. This demonstrates the BALANCED EXTENSIVENESS of the MIDDLE DISTANCE in/of SPACE as NECESSARILY and FUNDAMENTALLY electromagnetic/gravitational (IN BALANCE). GREAT !!! Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. THE SUN (including the ORANGE SUN) AND THE EARTH (including the GROUND) are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma. Objects fall at the same rate, AS the SPEED OF LIGHT is RELATIVELY CONSTANT AS WELL. GREAT !!! It ALL makes perfect sense. The stars AND PLANETS are POINTS in the night sky. F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The balance of being AND EXPERIENCE is ESSENTIAL. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Indeed, the ability of THOUGHT to DESCRIBE OR RECONFIGURE sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience. THOUGHTS ARE INVISIBLE. Magnificent !!! THE SELF represents, FORMS, and experiences a COMPREHENSIVE approximation of experience in general by combining conscious and unconscious experience. THE EYE IS THE BODY, AND the DOME of a person's EYE is ALSO VISIBLE. BALANCE AND completeness go hand in hand. Indeed, the INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. Really THINK about it all. A PHOTON may be placed at the center of THE SUN (as A POINT, of course), as the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED. "Mass"/ENERGY are linked AND BALANCED. OVERLAY what is THE EYE in BALANCED RELATION to/WITH what is THE EARTH. NOW, LOOK at what is the semi-spherical, translucent, QUANTUM GRAVITATIONAL, AND BLUE SKY. The DOME of a person's EYE is ALSO VISIBLE. GREAT !!! THE EARTH is ALSO BLUE. Excellent !!! (Consider the black space of what is THE EYE as well, of course.) The ultimate unification (AND UNDERSTANDING) of physics/physical experience combines, BALANCES, and includes opposites. BALANCE AND completeness go hand in hand. Really THINK about it ALL. Great !!! There is no outsmarting the GENIUS of dreams. Dream experience is/involves true/real QUANTUM GRAVITY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Very importantly, outer "space" involves full inertia, AND it is fully invisible AND black. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. ACCORDINGLY, a given PLANET (INCLUDING WHAT IS THE EARTH) sweeps out equal areas in equal times; AND this is THEN consistent with/as F=ma, E=mc2, AND what is PERPETUAL MOTION; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. INDEED, GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. IT IS PROVEN. GREAT !!! ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. By Frank DiMeglio
Letter K = pause Even the professor would need to pause the screens with multiple equations if it was the first time she'd seen 'em. I like the rapid fire delivery so I can figure it out and not have to wait for someone to half-explain it.
Sabine is very clear and understandable. She is a very good physics teacher. Too bad there were not more Sabines back when I was a physics student in the 1970s.
Vielen Dank für das Hochladen. Ich werde bald dieses Modul an der Universität nehmen. Dieses Video hilft als kleiner Einstieg zu diese Welt der Differentialgleichung.
Thank you Dr., someone said science is fun when described by a person who loves knowledge. He was right. Thank you for the content. It started off some gears in my head for sure.
Great video, Sabine! I had Calc I and started Calc II when I had to drop out of school for awhile. Someday I'll go back and learn more math. Great outfit, as always!
I'm not a math lover by any means, but I had fun in calc when we were doing the shapes of graphs and then in ecology I learned all these certain curves fit patterns of living things in nature, and my mind was blown. However, it really let me understand how scary the human population growth is, which is exponential and this exponential growth also fits with C02 emissions and im sure it will fit the methane release once the permafrost melts beyond the point of no return as well as the frequency of pandemics.
They are a great approximation for how any system that has a living component in it will evolve/change, and are just fun on their own, Thanks for this wee video.
@@plemli Sound like you also want to hear you way it again. Feel free to use the link directly to the timestamp that I provided in my original comment. And you're welcome!
Why does any man-made tool work? It was designed to work to solve a problem at hand. Your real question is: Why is the universe consistent and follows "rules" that allow us to apply our mathematical tools to discern them?
And also, why does the mathematical order present in scientific observations require such sophisticated math? But these are metaphysical questions which do not concern physics. Physics starts with what is given, namely objective observations.
Math is a coherent language in which you can speak about the world. Just as you can speak in German or French. German or French describes the world, why? Because that's what language does by definition. Therefore your inquiry is tautological. And for instance if I wanted to describe human behavior I would refer to Shakespeare before I'd refer to differential equations, the language of Shakespeare being more descriptive than numbers.
Excellent video. I studied differential equations (or "Diffy Qs" for short here in the U.S.) decades ago, and needless to say, my grasp of them loosened quite a bit over the years. This was a thoroughly enjoyable refresher. refresher.
Thank you for these very insightful videos it would be nice if you actually solved a differential equation so that we could get a feel for how it is done
The main thing to always remember when discussing how our methods describe the universe is that we are working with models, our map of the land, not the land itself. Many people learn about the seemingly probabilistic nature supposedly intrinsic in quantum mechanics and assume that therefor the universe cannot be deterministic. It is well possible to model a deterministic universe in an indeterministic way, as we are not dealing with a description of reality but models that make predictions. Even if we can describe where a particle is 'likely' to end up with some probability density function, this does not imply the particle would end up anywhere else than where it does, as repeating the experiment with the same initial conditions is both impossible, and conceivable with global hidden variables and such which predetermine an outcome that our models do not and perhaps cannot account for. Einstein may well get his last laugh on the matter many would now call his biggest mistake.
Not only is Einstein right, but he already fund the way to build an inconsistency free quantum theory. But at his time, the tools weren't available to fully develop this theory. Today they are, but people look the other way and parrot: "shut up and calculate."
Except nobody can get the last laugh in the game we call physics. Our current understanding, aka experimental evidence, suggests that hidden variables don't exist. It is true that future evidence may show that we do indeed have a variant of them and maybe even construct a purely deterministic version of quantum mechanics. But as you said that's ultimately still a "map of the land, not the land itself" we are speaking of. In that future one could argue that perhaps everything seems deterministic just like classical thermodynamics displays deterministic behaviour while being intrinsically probabilistic. Physicists can only talk about the map - as the map is what we can know of the universe while being part of it. Speculations on the nature of the land goes meta, we start to get into the realm of philosophy, which is fine of course - most physicists have their interpretations explaining the whys of a theory - but one also should be aware of the distinction. Also, Mr. Massé, if you're reading this, "shut up and calculate" was never that popular. Physicists are part mathematician, part engineer and part philosopher. Shut up and calculate helps the engineer in us to innovate and produce results but the other two parts are always working in the background trying to understand the deeper meaning of said calculations.
Amazing explanation. The examples were really well picked to illustrate the essence of differentials equations in general, without falling head first into a sea of calculus. I do notice that all tutorials on TH-cam are very fast, but fortunately it is easy enough to pause or wind back.
@@DerTaran pbs space time's episode on "could life evolve inside stars?" Search it on TH-cam. You will see her the host talking about her at the comment responses
I know I know, it's just a little fast for the classroom; but unlike the classroom you can just press 'rewind'. She's really excellent. I really enjoy her work. Her delivery is somewhat different I guess. Being German helps. For some reason, people think German folks are smarter than all the rest of us. They're not, it's just that that's what people 'think'; it works ! 🙂
I only just discovered you and your videos. You are an amazing human being. If you ever travel to Australia, I'm a content creator who would love to collab!
As a senior in high school in the sixties I took advanced math. we covered differentiation the long way, the short way, and then integration. In physics we were studying S=1/2AT**2 when I recognized it as an integral! F, F', & F" were really force, velocity and distance. Calculus made a lot more sense after that. Doc, thanks for all your good work.
This video sponsored by 'Hossenfelder Threads' For the best in avant garde clothing for today's scientifically-informed youth, think 'Hossenfelder Threads'. Today's featured top is 'Forward-Slash on Robin's Egg Blue'. A semi-sequined backslash over a resplendent field of blue is modeled by Sabine Hossenfelder, one of our brightest minds in the emerging field of theoretical physics/ modelling.
The world changes both spatially and dynamically and we want to be able to predict how it will change under certain circumstances. Continuous change is represented by derivatives hence the equations of change involve derivatives. Hence the changing world is modeled using differential equations.
The most cool thing is that we solve diff E q with verry simple neural network. We can even do that where we do not have the equation but only sampled points.
I'm in my seventies and never got passed college algebra. My best childhood friend was an electrical engineering student and was a bit egotistical about it in comparison to the other engineering majors, i.e., chemical, mechanical, etc. He considered Civil engineers to be at the bottom. He would have lengthy conversations with my dad and admitted to me privately...your dad is pretty smart for a Civil engineer ! Thank you Sabine.
My differential equations class turned into a real bone of contention. For the three of us who were Physics majors it was a required course in our second year, but for the 20 math majors it was an elective that they took in their final year. All throughout the course the professor would make references like, "As you remember from your linear algebra days," before going off onto a linear algebra-related tangent. Well, that was fine and dandy for the math majors who had had linear algebra, but for the three of us who were the only ones *required* to take differential equations, we hadn't had linear algebra! We were required to take Calc 1, 2, 3, and DiffEQs right off the bat and everything after that was just Physics courses. After about a month of this we finally complained about it and made it clear that if he was going to require us to know about a course we hadn't had any opportunity to take he'd darn well better explain what he was talking about and if the math majors were bored, that was too bad.
This actually answered my question I asked on your post. I suppose, in a way, it doesn't really matter what you think you know in or about physics. It's more about what you are trying to do with physics at the moment.
I was thinking about the deterministic nature of differential equations as I watched your explanation; something I hadn’t even understood until this video, thank you! When you mentioned it I thought of the philosophy of determinism, but then decided not to comment as I assumed it was too much of a tangent for a primarily math/physics channel... then you ended with a promise to explore free will and I exclaimed out loud with joy! Looking forward to your next video Dr. Hossenfelder.
It's been almost four decades since I took DifEq in college and have had no need to use this level of math during my engineering career, although, I did use differential and integral calculus now and then.
i'm very interested to know, what "aspect" or practice is most used in engineering? is most of it spent conceptualizing and thinking? sorta "dreaming" up solutions if you will? or mostly spent building, putting parts together to achieve a bigger goal?
Thank you Dr. Hossenfelder, very important that you talk about the basic tool of the trade. You made a clean and linear explanation of what a differential equation is; but my feeling is, common people may not know, or recall, what a derivative is; and therefore they can't grasp in full anything you explained beyond that point. Differential equations, for being a fundamental tool discovered more than 400 years ago, should be taught - at least conceptually - in primary schools, not only at University level and for some types of degree. Early in life I realised that knowing the concepts of operating with functions - by using differential equations - is not only a skill needed to design an electronic filter, calculate a libration point in the sky, or any of the myriad of other possible tasks; this knowledge influences deeply the way one person perceive and interact with the world; this is why I consider an error the fact that only an handful of people are conversant with these tools. I greatly appreciate your video meant to spread the knowledge of differential equation. Thanks.
It's precisely for this reason that they aren't taught, beyond the known solutions of the second order ODE. Now the theory of general differential equations is not that easy.
A differential equation is a shorthand that tells what the definite integral will look like. Since there are no infinitesimals in nature, one actually needs to study the definite integral to understand cause and effect. The boundary conditions (initial values) are where the integral connects to reality. Nature is continuously summing things up. - Integrating the acceleration equation, one gets a velocity equation with an integration constant (initial velocity TBD). - Integrating the velocity equation, one gets a distance equation with one more integration constant (initial position TBD).
Watching this my brain said this to me. A function can appear chaotic because sometimes the function is altering the ocurrence of a property, but sometimes it switches to altering the amplitude of the property. It's like it's flipping between digital to analog and back again.
0:35 That's one of the reasons they are powerful: they allow us to predict, provided the mathematical model correctly describes the physical system. Amazing :)
Science is so much more interesting when explained by somebody who obviously loves knowledge and is dedicated to spreading it.
Spreading knowledge. Knowledge is contagious. So introduce teachers in a society of uneducated. Then let’s call learning E(0).
E nought.
She is lying about the fundamentals of physics.
THE TOP DOWN (AND MATHEMATICAL) UNIFICATION OF PHYSICS/PHYSICAL EXPERIENCE IS PROVEN:
F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational (IN BALANCE). Therefore, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. In other words, gravitational force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (BALANCE AND completeness go hand in hand.) Consider what is THE SUN, and consider what is c (A POINT, A PHOTON). Now, consider our direct experience of what is NECESSARILY the BALANCED MIDDLE DISTANCE in/of SPACE. Perfect. Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE.
BALANCED inertia/INERTIAL RESISTANCE is fundamental, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The rotation of THE MOON MATCHES it's revolution, AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. This demonstrates the BALANCED EXTENSIVENESS of the MIDDLE DISTANCE in/of SPACE as NECESSARILY and FUNDAMENTALLY electromagnetic/gravitational (IN BALANCE). GREAT !!! Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. THE SUN (including the ORANGE SUN) AND THE EARTH (including the GROUND) are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma. Objects fall at the same rate, AS the SPEED OF LIGHT is RELATIVELY CONSTANT AS WELL. GREAT !!! It ALL makes perfect sense. The stars AND PLANETS are POINTS in the night sky.
F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The balance of being AND EXPERIENCE is ESSENTIAL. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Indeed, the ability of THOUGHT to DESCRIBE OR RECONFIGURE sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience. THOUGHTS ARE INVISIBLE. Magnificent !!! THE SELF represents, FORMS, and experiences a COMPREHENSIVE approximation of experience in general by combining conscious and unconscious experience. THE EYE IS THE BODY, AND the DOME of a person's EYE is ALSO VISIBLE. BALANCE AND completeness go hand in hand. Indeed, the INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. Really THINK about it all.
A PHOTON may be placed at the center of THE SUN (as A POINT, of course), as the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY.
Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED. "Mass"/ENERGY are linked AND BALANCED. OVERLAY what is THE EYE in BALANCED RELATION to/WITH what is THE EARTH. NOW, LOOK at what is the semi-spherical, translucent, QUANTUM GRAVITATIONAL, AND BLUE SKY. The DOME of a person's EYE is ALSO VISIBLE. GREAT !!! THE EARTH is ALSO BLUE. Excellent !!! (Consider the black space of what is THE EYE as well, of course.)
The ultimate unification (AND UNDERSTANDING) of physics/physical experience combines, BALANCES, and includes opposites. BALANCE AND completeness go hand in hand. Really THINK about it ALL. Great !!!
There is no outsmarting the GENIUS of dreams. Dream experience is/involves true/real QUANTUM GRAVITY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY.
Very importantly, outer "space" involves full inertia, AND it is fully invisible AND black.
Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. ACCORDINGLY, a given PLANET (INCLUDING WHAT IS THE EARTH) sweeps out equal areas in equal times; AND this is THEN consistent with/as F=ma, E=mc2, AND what is PERPETUAL MOTION; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. INDEED, GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. IT IS PROVEN. GREAT !!! ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY.
By Frank DiMeglio
Frank DiMeglio is RECOGNIZED as having surpassed Newton and Einstein.
Frank DiMeglio why is the fact that Earth’s moon is tidally locked with Earth’s rotation relevant to anything relating to electromagnetism *or* gravity? It’s just something that happens to be true at this moment in time, it wasn’t always true in the past and won’t continue to be so in the future.
Also, your erratic and confusing use of ALL CAPS makes your writing exceedingly difficult to decipher; true genius knows how to communicate ideas effectively.
Dr. Hossenfelder, I was great at working out Differential Equations in my youth (I'm now 78). I stumbled on your video and decided to see if I have enough brain left to follow it through. I do, thank you. I love your passion of math and science, I have never lost my own. I look forward to whatever else you can reawaken in me.
I respect how you don’t assume familiarity by addressing her by her Christian name.
Even more interesting is her piece on how the so-called multiverse fantasy is pure religion, but perhaps that is stating the obvious.
Great for you, Sir. One thing to play bingo, another to solve ODE's.
@@greggstrasser5791 what
@@yasyasmarangoz3577 What what.
I struggled so much last semester attempting to understand why we were solving these differential equations and what the outcomes meant. I was often told "If you see this, do this and you'll do fine." But "Why!!?" Thank you Dr. Hossenfelder, it fills me with joy, I finally understand why.
*Opens differential equations textbook*
The lack of a "why" was always so frustrating lol these channels are a blessing
If you’re told ‘see this, do this...’ you’ve got an awful teacher who’s throwing you under the bus. Can’t believe that in this day and age
I'm happy in return I could be of help!
@@paulcarson7860 You exactly describe my personal experience 55 years ago. Never given any background, context or purpose for differential equations, but was taught to go through the motions. One of the greatest disappointments of my education. Thank you, Sabine.
@@unthawedwater747 The lack of "why" is often because you need to learn the subject material first before you can really explore the understanding of "the why" and, as a student, it is kinda your responsibility to figure out why you are doing things.
Every time I watch Sabine's videos, I realize how little I know and that I should have applied myself more in mathematics and the sciences.
ditto!
What's stopping you from doing it now?
I used to ask questions, but everybody including professors were busy in preparing you for the "exam" and getting more marks in exam rather than the actual meaning behind these Mathematical concepts
@@nickharrison3748 Why blame your teachers when you had the ability to grab a shovel and dig?
@@Mastermindyoung14 it was hard back then, pre Internet era, you had to read multiple books and also learn other subjects. If we have to do everything, why do you need teachers with specialized fields then?
I wish I had a “teacher” that could actually explain this subject as Sabine has done.👍
I took several courses in differential equations, many decades ago and I really enjoyed using them to model various behaviours. Partial differential equations and even stochastic differential equations I found even more interesting. I have forgotten almost all of that stuff in the time since.
Many people don’t know when buying shocks for their cars in reality they buying just the dumping coefficient of solution of a differential equation of an oscillating system created by car weight, spring and a hole in the ground.
show off!
Indeed! The dumping coefficient!! That explains so many things about cars!
Sorry, couldn't help myself.
And, somewhat surprisingly, -many- the vast majority of people do not care. 😁
Trying to be funny
@UFB-NFW X Damping haha
That is the fastest summary of the use of differential equations I have ever encountered. How did you do it all in one breath? It is also the most concise and cogent explication of the fact that differential and partial differential equations are not esoteric but powerful tools for everyday use.
Thank you Sabina. I shall make an offering at your shrine.
Student: What is the meaning of life?
Dr.Hossenfelder: Differential Equations! 😂😂
This is what passes for thinking?
@@johnsmith1474 That's a little rude my man
There is no meaning in life of speculative physicists ... that's why differential equations... If there were, the equations would called the equality equations...lol
😂. Funny mate.
It’s not rude guys. Dr h encouraged the joke. And you know German jokes are no laughing matter.
@@shoopinc The physicists think they have the panacea and the jouvence spring together, any other idea or concept is crackpot or superstition. _That_ is rude.
I've been subscribed to Sabine for just over a year now an she's definitely the most charismatic science popularisers. When is she getting her own PBS or Netflix spot? I'm ready for it.
PBS & Netflix are part of the problem.
@@greggstrasser5791 Explain?
@@fesimco4339
All the stuff Dr Hossenfelder talks about where scientists are touting questionable science is propagated by mainstream media.
If it’s on mainstream media, it’s not trustworthy.
@@greggstrasser5791 I see what you're saying but that last bit is over the top right?
@@fesimco4339
Not really. “Trust” means you don’t question it.
I don’t believe any of it anymore.
Is gravity a byproduct of the warping of “space-time” or an interaction with Higgs? Both are presented as “fact.”
I am mathematically impaired. I am incapable of grasping even the most basic mathematical concepts. I can understand everything in videos of this type up to and until the program starts to produce the mathematical reasoning behind every event in science. My grasp of numbers stopped at simple arithmetic. I wish it wasn't so, but at 81 I'm too old and set in my ways for anything to change me now. But, I do comprehend everything she is trying to explain. Sabine is a great explainer in a renowned history of great explainers.
so, you don't understand basic math but was able to understand DIFFERENTIAL EQUATIONS from a 10-minute video ? You are the same age and at the same "reasoning dexterity" as Biden 👍
Thanks for your deep insights in your TH-cam videos.
If you like that particular exposition, you might also like her exposition of how the what is called "multiverse" fantasy is pure undiluted religion, which of course it is
If I hadn’t essentially failed Algebra 1 twice back in high school, I’m sure I’d enjoy your videos even more.
Your presentations are the best, and I feel smarter for having watched them. 🧬🧪👩🔬
"Differential equations."
Dammit, now I can't stop saying it.
Great video as usual!
For the sake of some readers, I will mention that you might even say that the word "initial" in "initial conditions" refers to things you know at the start of solving the problem. You can also call initial conditions "boundary conditions" or "constraints", which simply tell you some extra information about the system, and these help you pick which one of the many possible solutions best fits the particular case you are considering.
yes boundary conditions is the best description
I guess which term one uses depends on whether one is a "time" person or a "space" person.
“Boundary conditions” is a good general term, because you might be solving the equations under a variety of scenarios. For example, instead of starting at an initial time and extrapolating forwards, you might have observations at a given time (e.g. the present) and are trying to extrapolate backwards into the past. “Boundary” is a more general term than “initial” or “final”. And yes, it can also include spatial boundaries as well.
YES! Initial conditions, like weather conditions (or a double pendulum for a simple system) have feedback loops between multiple variables, and small errors in initial conditions completely dominate outcomes after some period of time.
Perhaps it should be also emphasized that, contrary to what a student may be lead to think from the calculus experience of solving explicitly differential equations via a bunch of tricks, *in real life science one rarely solves a differential equation* in that sense. In fact, it is feasible to find explicit solutions only for very restricted classes of such equations.
Even in the very theory of (ordinary or partial) differential equations in Mathematical Analysis, one is almost never able to find explicit solutions, and finding the latter is not the goal anyway: the goal is to understand the properties of the solutions (individually or of the whole space they form).
And even in the case in which it is possible to "write down" a solution (say by expressing it via a Fourier expansion), the expression is seldom useful in order to understand its properties.
As for applied mathematics and physics, again, one typically doesn't solve DEs explicitely (physicists say "analytically"). Methods of numerical analysis are used instead, that allow one to get a numerical approximation (typically by using an extremely powerful computer).
Models! "All models are wrong, but some are useful" :-)
Those words should be printed in BOLD FACE type on the first page of every textbook on ordinary differential equations. The "tricks" are neat, but the real solution is had by grinding it out numerically.
@@markotrieste I was just thinking that and you beat me to it. It’s about projecting, not predicting, and differential equations are used every second in infectious disease modelling
Had to scroll down pretty far to find your comment.
Engineering students take 3 years of calculus and one year of DiffEq
when they get their first job where they have to do something in the real world, they quickly discover the real world is not linear, it is partly chaotic, it is somewhat random, and the initial conditions are extremely difficult to define
what you end up with from those 4 years of math is at BEST an approximation, never an exact 'correct' answer
its demoralizing for engineers to discover after they believed they would be able to control everything with carefully designed systems
what you end up with is a career steeped in probability and statistics
@@kenwittlief255 what kind of engineering are you talking about?
Interestingly enough, this topic hit me on the head when I started my first upper-division class in Physics at UCLA in 1968. I had taken all of the required math classes, such as calculus and so forth, for a Physics Major and I went into my first day of MECHANICS 101, the baseline Physics class for essentially everything else in my Physics Major to get my Bachelor Degree. I sit down and the class starts. The professor puts the HAMILTONIAN Differential Equation on the blackboard, one of the fundamental formulae for solving a LOT of Physics problems and absolutely essential to understand for this and all later Physics classes. A small problem, though: I had not taken ANY differential equations classes because they were not on the required list! I said to the professor: "That is a differential equation. I have not had any classes on how to solve them." He looked at me and said, with no exaggeration, "Then you had better learn fast!" I was so angry that I stomped all the way to the secretary of the Director of the Physics Department of UCLA (now combined with Astronomy) and stated that they have to change their requirements to warn students that they need to take Differential Equations BEFORE getting into upper-division classes. She said she would talk to the Director about this and I left. I do not know if it ever happened, though. What did happen for me was taking two classes in this end-to-end by the best professor I ever had, Dr. David Sanchez, and deciding to take a few more math classes to get a double bachelor degree in Math and Physics, so it did have a good result in the end. But I still get mad when I think about it...
Sabine is a gift to us thinking people. I have enjoyed many of her short physics videos, and now this one really brings those ancient studies back to life with new vision. Thank you so much.
These videos are well done
I liked the part where you said "Differential Equations"
Can you be more specific plz?
I, too, enjoyed that part
I like the way she says certain words. So far, my favorite is "iron.'
She pronounces the German ones correctly, too, like "Einstein," with the "sh" sound.
I don’t think I’ve ever been looking forward to a next TH-cam video as much as I am for your one next week!
I think you have no free will do decide: looking the next video or not :-)
I know I am subscribed to a high quality content creator when I search something on TH-cam and among the top search results is a video from a channel I'm already subscribed to. My only regret is that I didn't find this channel sooner.
A good educator is worth more than a quadrillion Kardashian.
What is a Kardashian?
@@MichaelOZimmermannJCDECS Uh, no apostrophe, to be exact.
Stfu man . Don't compare
Editot
@@satvikvarun6386 no sense of humor?
No brains?
Angry and rude?
Makes sense.
@@tillabakos2248 what I'm trying to tell is that is that what you commented is true. BUT comparing a teacher with Kardashian is an insult to the teacher. (Hope u get my point)
Studying in university : differential equations.
😂😂😂 loved that . Truth 👍
Been there, done that. Good luck
It's like TH-cam is reading my mind or something
Im getting my PhD in left-handed puppetry. We don't do math! 🙂
@@darylallen2485 😂
If you want to understand how nature works, do learn calculus: there's no shortcut 😉Tnx Doc Sabine 👍
Not true. Endless numbers of people good at calculus have no clue how "nature" works. And the results of man calculations hold little insight into the mechanisms behind the numbers. The ability to do a calculation is not equivalent to understanding a thing.
It kills me that I could have learned calculus, *should* have but I didn't believe in my own intelligence and was trapped in a religion that discouraged higher learning. It would have greatly added to my other interests in physics, astronomy and now, evolution.
@@johnsmith1474 Sure, and despite the fact that I own a hammer and nails and have a whole bunch of wood, don't expect me to be doing any decent carpentry anytime soon. Just because someone has a tool, does not mean they can use it effectively.
Calculus is a necessary (but not sufficient) tool for understanding how nature works. And this cannot be stressed enough: calculus (and maths in general) is *faaaar* more than than doing calculations. In 2020, an era where mankind is drowning in transistors, numerical calculation is probably the least useful thing an understanding of maths gives you.
@@johnsmith1474 he said it is a necessary tool to have, not that having it gives you the understanding it can be employed to achieve. And, of course, you need other tools, but he didn't say you don't... one really has to wonder what made you so determined to conflate opposite-moving logics like that
If you truly want to understand how nature works, study Zen... 👈
I have much suffered in grade 12 with these differential equations. The examples you gave did refresh my memory somehow and I wish I had had this kind of expose at the time. Well done!
Before watching this I wasn't sure what Differential Equations were. I still don't know but I love watching Sabine. I will have to watch this a few more times. Thanks Sabine.
So far I had differential equations in nuclear physics/radioactivity, on ossications/waves and in classical mechanics newtons laws. But I've also seen them in the navier stokes equations and einsteins general theory of relativity, as well as in the schrödinger equations. They are literally everywhere when you study physics, and they are the branch of maths I love the most.
Great video about "Diffe Qs". One of the things I remember when I took the course is that many differential equations cannot be solved using analysis. Please do a video on this. I have been viewing many of your videos and it's obvious you are an accomplished Theoretical Physicist with talent to teacher. That's why I ask.
It's "Diff Eq." Not Diffe or Diffy Q
Differential equations, linear algebra, probability/statistics, and number theory--four pillars for describing and understanding so much of what we see around us.
They are the foundation of any education in Maths and Sciences... and Engineering.
I don't really know many applications of number theory. Except in cryptography.
In addition to being informative and educational, your videos are always a fun watch due to the subtle humour sprinkled in here and there. Your channel is easily one of my favourites on TH-cam!
Hello there Sabine. Thank you for your simplified, easy to understand explanation. Brilliant!
Is she not explaining how it is possible to calculate how mutually dependent causes and effects change?
I simply switched off my associative apparatus when various bullies were trying to force me to learn what is called mathematics, but if they had explained to me or what differential equations might be useful, I might not have dismissed the entire subject as having no relevance or importance to me whatsoever - which as it has turned out, has been the case. I have never needed any kind of equation in my entire life or mathematics for that matter. I was forced to learn about differential equations and of course simply flat out refused to do so, because I could not see the point of them, or mathematics generally
This is way above my pay grade but I congratulate you for explaining this in a way I could understand (kind of).
I just realized how the way math was taught in school had completelly turned me off of exploring it, and only made me feel inadequate and stupid. It was a humiliating experience that caused me to ignore the topic for 40 years. I wasn't even trying, even though I knew I should be able to understand at least the basics. Now I'm finally learning the basics. This would have been easy - thanks for making so much knowledge accessible. I really like your calm style.
0:56 "To get an idea for how differential equations work, let us look at a simple example: The spread of a disease though the population".
Fast forward to 01:46, after the "simple explanation"... and my brain is swimming. Thanks for keeping it so simple. 😵💫😵💫😵💫
Ah yes... Thank you Frau Hossenfelder for that "simple example". Haaaaa! 🤯🤯🤯
Ma'am you are unique teacher in the world
These kind of video pave the way of a new type of popular education. Not replacing, but adding to the current system.
THE TOP DOWN (AND MATHEMATICAL) UNIFICATION OF PHYSICS/PHYSICAL EXPERIENCE IS PROVEN:
F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational (IN BALANCE). Therefore, gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. In other words, gravitational force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (BALANCE AND completeness go hand in hand.) Consider what is THE SUN, and consider what is c (A POINT, A PHOTON). Now, consider our direct experience of what is NECESSARILY the BALANCED MIDDLE DISTANCE in/of SPACE. Perfect. Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE.
BALANCED inertia/INERTIAL RESISTANCE is fundamental, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The rotation of THE MOON MATCHES it's revolution, AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. This demonstrates the BALANCED EXTENSIVENESS of the MIDDLE DISTANCE in/of SPACE as NECESSARILY and FUNDAMENTALLY electromagnetic/gravitational (IN BALANCE). GREAT !!! Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. THE SUN (including the ORANGE SUN) AND THE EARTH (including the GROUND) are linked AND BALANCED opposites, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY. "Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent with/as what is BALANCED electromagnetic/gravitational force/ENERGY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma. Objects fall at the same rate, AS the SPEED OF LIGHT is RELATIVELY CONSTANT AS WELL. GREAT !!! It ALL makes perfect sense. The stars AND PLANETS are POINTS in the night sky.
F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE. E=mc2 is DIRECTLY AND FUNDAMENTALLY DERIVED FROM F=ma, AS ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. The balance of being AND EXPERIENCE is ESSENTIAL. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/ENERGY IS GRAVITY. Indeed, the ability of THOUGHT to DESCRIBE OR RECONFIGURE sensory experience is ULTIMATELY dependent upon the extent to which THOUGHT IS SIMILAR TO sensory experience. THOUGHTS ARE INVISIBLE. Magnificent !!! THE SELF represents, FORMS, and experiences a COMPREHENSIVE approximation of experience in general by combining conscious and unconscious experience. THE EYE IS THE BODY, AND the DOME of a person's EYE is ALSO VISIBLE. BALANCE AND completeness go hand in hand. Indeed, the INTEGRATED EXTENSIVENESS of THOUGHT (AND description) is improved in the truly superior mind. Really THINK about it all.
A PHOTON may be placed at the center of THE SUN (as A POINT, of course), as the reduction of SPACE is offset by (or BALANCED with) the SPEED OF LIGHT, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY.
Gravity AND ELECTROMAGNETISM/ENERGY are linked AND BALANCED. "Mass"/ENERGY are linked AND BALANCED. OVERLAY what is THE EYE in BALANCED RELATION to/WITH what is THE EARTH. NOW, LOOK at what is the semi-spherical, translucent, QUANTUM GRAVITATIONAL, AND BLUE SKY. The DOME of a person's EYE is ALSO VISIBLE. GREAT !!! THE EARTH is ALSO BLUE. Excellent !!! (Consider the black space of what is THE EYE as well, of course.)
The ultimate unification (AND UNDERSTANDING) of physics/physical experience combines, BALANCES, and includes opposites. BALANCE AND completeness go hand in hand. Really THINK about it ALL. Great !!!
There is no outsmarting the GENIUS of dreams. Dream experience is/involves true/real QUANTUM GRAVITY, AS ELECTROMAGNETISM/ENERGY IS GRAVITY.
Very importantly, outer "space" involves full inertia, AND it is fully invisible AND black.
Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. ACCORDINGLY, a given PLANET (INCLUDING WHAT IS THE EARTH) sweeps out equal areas in equal times; AND this is THEN consistent with/as F=ma, E=mc2, AND what is PERPETUAL MOTION; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. INDEED, GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. IT IS PROVEN. GREAT !!! ALL of SPACE is NECESSARILY electromagnetic/gravitational IN BALANCE, AS ELECTROMAGNETISM/ENERGY IS GRAVITY. F=ma AND E=mc2 PROVE that ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/ENERGY.
By Frank DiMeglio
Hossenfelder is knowingly and deceitfully lying about physics.
Excellent content. A little slower for slow thinkers like myself would be nice.
Settings----->Playback Speed----->0.50 or 0.25......You're welcome.
@@buzz-es *You’re welcome.
You’re welcome.
@@MoebiusUK T h a n k y o u
Letter K = pause
Even the professor would need to pause the screens with multiple equations if it was the first time she'd seen 'em.
I like the rapid fire delivery so I can figure it out and not have to wait for someone to half-explain it.
Beauty of personal media like TH-cam is you can watch it 100 times.
Sabine is very clear and understandable. She is a very good physics teacher. Too bad there were not more Sabines back when I was a physics student in the 1970s.
Vielen Dank für das Hochladen. Ich werde bald dieses Modul an der Universität nehmen. Dieses Video hilft als kleiner Einstieg zu diese Welt der Differentialgleichung.
Thank you for your work!
I’m inspired to pull out my old math books for a deep review.
Absolument passionnant! Merci Mme Hossenfelder pour votre travail remarquable!
Thank you Dr., someone said science is fun when described by a person who loves knowledge. He was right. Thank you for the content. It started off some gears in my head for sure.
Great video, Sabine! I had Calc I and started Calc II when I had to drop out of school for awhile. Someday I'll go back and learn more math. Great outfit, as always!
I'm not a math lover by any means, but I had fun in calc when we were doing the shapes of graphs and then in ecology I learned all these certain curves fit patterns of living things in nature, and my mind was blown. However, it really let me understand how scary the human population growth is, which is exponential and this exponential growth also fits with C02 emissions and im sure it will fit the methane release once the permafrost melts beyond the point of no return as well as the frequency of pandemics.
I haven’t heard anyone talk about “DiffyQ” in a half century.
They are a great approximation for how any system that has a living component in it will evolve/change, and are just fun on their own, Thanks for this wee video.
Fantastic. Its a subject that it so overlooked in popular science talk. Conceptually it is very simple compared to what we would assume.
0:41 I don't know what a "wideo" is, but I want to hear her say it again...
:-)
... it's a Funktshion of the Uniwerse. What isn't to love about this impeccable English with a hint of charming accent ?
@@plemli Sound like you also want to hear you way it again. Feel free to use the link directly to the timestamp that I provided in my original comment. And you're welcome!
Danke Sabine!
It would be interesting to hear your opinion about “why” the universe has a mathematical nature. Why do differential equations work?
“Why” assumes the universe IS mathematical in nature.
This is debatable and not a given fact.
Why does any man-made tool work? It was designed to work to solve a problem at hand. Your real question is: Why is the universe consistent and follows "rules" that allow us to apply our mathematical tools to discern them?
And also, why does the mathematical order present in scientific observations require such sophisticated math?
But these are metaphysical questions which do not concern physics. Physics starts with what is given, namely objective observations.
Math is a coherent language in which you can speak about the world. Just as you can speak in German or French. German or French describes the world, why? Because that's what language does by definition. Therefore your inquiry is tautological. And for instance if I wanted to describe human behavior I would refer to Shakespeare before I'd refer to differential equations, the language of Shakespeare being more descriptive than numbers.
If the universe were wholly chaotic, it would not support thinkers to ask the question.
Ich bin begeistert von der Klarheit und Präzision, mit der Frau Hossenfelder komplexe Sachverhalte erklärt.
Excellent video.
I studied differential equations (or "Diffy Qs" for short here in the U.S.) decades ago, and needless to say, my grasp of them loosened quite a bit over the years. This was a thoroughly enjoyable refresher. refresher.
Is it deterministic that we will have another great video next week ? Difficult to say in this chaotic world 🙂. Thank you, very well explained.
😀
😄
fantastic approaches to every thing difficult...we wish we had teatcher like YOU
I'm obsessed with this channel. Thank you Sabine for helping me renew my education in my favorite subjects from school!
Danke für Ihre Mühe jede Woche!
Ihre Erklärungen öffnen mir immer neue Sichten auf die Natur.
Thank you for these very insightful videos it would be nice if you actually solved a differential equation so that we could get a feel for how it is done
That's just maths tho
And proving the solving techniques would have taken some time
The main thing to always remember when discussing how our methods describe the universe is that we are working with models, our map of the land, not the land itself. Many people learn about the seemingly probabilistic nature supposedly intrinsic in quantum mechanics and assume that therefor the universe cannot be deterministic. It is well possible to model a deterministic universe in an indeterministic way, as we are not dealing with a description of reality but models that make predictions. Even if we can describe where a particle is 'likely' to end up with some probability density function, this does not imply the particle would end up anywhere else than where it does, as repeating the experiment with the same initial conditions is both impossible, and conceivable with global hidden variables and such which predetermine an outcome that our models do not and perhaps cannot account for.
Einstein may well get his last laugh on the matter many would now call his biggest mistake.
Not only is Einstein right, but he already fund the way to build an inconsistency free quantum theory. But at his time, the tools weren't available to fully develop this theory. Today they are, but people look the other way and parrot: "shut up and calculate."
Except nobody can get the last laugh in the game we call physics. Our current understanding, aka experimental evidence, suggests that hidden variables don't exist.
It is true that future evidence may show that we do indeed have a variant of them and maybe even construct a purely deterministic version of quantum mechanics.
But as you said that's ultimately still a "map of the land, not the land itself" we are speaking of.
In that future one could argue that perhaps everything seems deterministic just like classical thermodynamics displays deterministic behaviour while being intrinsically probabilistic.
Physicists can only talk about the map - as the map is what we can know of the universe while being part of it. Speculations on the nature of the land goes meta, we start to get into the realm of philosophy, which is fine of course - most physicists have their interpretations explaining the whys of a theory - but one also should be aware of the distinction.
Also, Mr. Massé, if you're reading this, "shut up and calculate" was never that popular. Physicists are part mathematician, part engineer and part philosopher. Shut up and calculate helps the engineer in us to innovate and produce results but the other two parts are always working in the background trying to understand the deeper meaning of said calculations.
SmaugtheStupendous Einstein would not laugh but simply say ‘I told you so’.
@@voom6996 The physicists are no longer philosophers, and that's why they are stuck.
You so much want the universe to be deterministic you'll believe in non-local hidden variables? I can't understand why people want to be automata.
Best intuitive explanation for differential equations I've ever seen!
This is a better overview than the one I received during the first lecture of my differential equations course.
Differential Equations: best of all possible worlds
Free Will: we must cultivate our garden
My answer to every question from now on
My son- “Dad can I get some money?”
Me- “differential equations”
Amazing explanation. The examples were really well picked to illustrate the essence of differentials equations in general, without falling head first into a sea of calculus. I do notice that all tutorials on TH-cam are very fast, but fortunately it is easy enough to pause or wind back.
Always informative, excellently elucidated, commendably communicate. Thanks again, Sabine
You lost me at "differential equations." (But I still love you.)
Watch some TH-cam videos on introduction to differential equations
great work!!! You are finally getting attention from large youtube channels. Do a collab pls
Is she? Can you give us some references? I would love to watch it.
Yes collabs would be great. Veritasium, thoughty2, or even numberphile or Scott Manley could be interesting!
@@olivier0092 Thanks and have a nice Sunday.
@@DerTaran pbs space time's episode on "could life evolve inside stars?" Search it on TH-cam. You will see her the host talking about her at the comment responses
This is very valuable. Thank you
I know I know, it's just a little fast for the classroom; but unlike the classroom you can just press 'rewind'.
She's really excellent. I really enjoy her work. Her delivery is somewhat different I guess.
Being German helps.
For some reason, people think German folks are smarter than all the rest of us. They're not, it's just that that's what people 'think'; it works ! 🙂
I only just discovered you and your videos. You are an amazing human being. If you ever travel to Australia, I'm a content creator who would love to collab!
spreading differential equations is now banned in Australia
It´s the end of the world as we know it, and I don´t feel fine...
NWO-control !!!
th-cam.com/video/CcIbb9MwFYI/w-d-xo.html
This is one of my favorite videos on this channel.
As a senior in high school in the sixties I took advanced math. we covered differentiation the long way, the short way, and then integration. In physics we were studying S=1/2AT**2 when I recognized it as an integral! F, F', & F" were really force, velocity and distance. Calculus made a lot more sense after that.
Doc, thanks for all your good work.
serious question: would anyone be willing to mentor me? i am so interested in math I think it all the time.
Have you checked out Fiverr?
What is your current level? Do you have discord or something?
This video sponsored by 'Hossenfelder Threads' For the best in avant garde clothing for today's scientifically-informed youth, think 'Hossenfelder Threads'. Today's featured top is 'Forward-Slash on Robin's Egg Blue'. A semi-sequined backslash over a resplendent field of blue is modeled by Sabine Hossenfelder, one of our brightest minds in the emerging field of theoretical physics/ modelling.
Don't mess with Sabine...you know she is beautiful...!
@@sidneyosborne947 Yes I know she is, I'm just poking a bit of fun at what she's wearing.
Can't wait for next week's video!
Thank you Dr Hossenfelder. I actually have an assignment on Differential Equations due just next week!
The world changes both spatially and dynamically and we want to be able to predict how it will change under certain circumstances. Continuous change is represented by derivatives hence the equations of change involve derivatives. Hence the changing world is modeled using differential equations.
really appreciate going back to basics and explaining things with such clarity for us who are unfamiliar with this stuff.
also a killer outfit.
The most cool thing is that we solve diff E q with verry simple neural network. We can even do that where we do not have the equation but only sampled points.
I'm in my seventies and never got passed college algebra. My best childhood friend was an electrical engineering student and was a bit egotistical about it in comparison to the other engineering majors, i.e., chemical, mechanical, etc. He considered Civil engineers to be at the bottom. He would have lengthy conversations with my dad and admitted to me privately...your dad is pretty smart for a Civil engineer ! Thank you Sabine.
My differential equations class turned into a real bone of contention. For the three of us who were Physics majors it was a required course in our second year, but for the 20 math majors it was an elective that they took in their final year. All throughout the course the professor would make references like, "As you remember from your linear algebra days," before going off onto a linear algebra-related tangent. Well, that was fine and dandy for the math majors who had had linear algebra, but for the three of us who were the only ones *required* to take differential equations, we hadn't had linear algebra! We were required to take Calc 1, 2, 3, and DiffEQs right off the bat and everything after that was just Physics courses. After about a month of this we finally complained about it and made it clear that if he was going to require us to know about a course we hadn't had any opportunity to take he'd darn well better explain what he was talking about and if the math majors were bored, that was too bad.
Excellent overview. Took me right back to my teenage years.
This actually answered my question I asked on your post. I suppose, in a way, it doesn't really matter what you think you know in or about physics. It's more about what you are trying to do with physics at the moment.
You are perhaps the most enjoyable speaker I've heard in quite some time! Great job!
Amazing how she does explain complex subjects in a simple manner !
Wow, another great video! I’ll be waiting for the book, “Easy Quantum Mechanics” 🤣👏👏 Thanks for the info!
I was thinking about the deterministic nature of differential equations as I watched your explanation; something I hadn’t even understood until this video, thank you! When you mentioned it I thought of the philosophy of determinism, but then decided not to comment as I assumed it was too much of a tangent for a primarily math/physics channel... then you ended with a promise to explore free will and I exclaimed out loud with joy! Looking forward to your next video Dr. Hossenfelder.
I now know as much about differential equations as I knew before I watched the video.
It's been almost four decades since I took DifEq in college and have had no need to use this level of math during my engineering career, although, I did use differential and integral calculus now and then.
i'm very interested to know, what "aspect" or practice is most used in engineering?
is most of it spent conceptualizing and thinking? sorta "dreaming" up solutions if you will?
or mostly spent building, putting parts together to achieve a bigger goal?
Thank you Dr. Hossenfelder, very important that you talk about the basic tool of the trade. You made a clean and linear explanation of what a differential equation is; but my feeling is, common people may not know, or recall, what a derivative is; and therefore they can't grasp in full anything you explained beyond that point.
Differential equations, for being a fundamental tool discovered more than 400 years ago, should be taught - at least conceptually - in primary schools, not only at University level and for some types of degree.
Early in life I realised that knowing the concepts of operating with functions - by using differential equations - is not only a skill needed to design an electronic filter, calculate a libration point in the sky, or any of the myriad of other possible tasks; this knowledge influences deeply the way one person perceive and interact with the world; this is why I consider an error the fact that only an handful of people are conversant with these tools.
I greatly appreciate your video meant to spread the knowledge of differential equation. Thanks.
It's precisely for this reason that they aren't taught, beyond the known solutions of the second order ODE. Now the theory of general differential equations is not that easy.
A differential equation is a shorthand that tells what the definite integral will look like. Since there are no infinitesimals in nature, one actually needs to study the definite integral to understand cause and effect. The boundary conditions (initial values) are where the integral connects to reality. Nature is continuously summing things up.
- Integrating the acceleration equation, one gets a velocity equation with an integration constant (initial velocity TBD).
- Integrating the velocity equation, one gets a distance equation with one more integration constant (initial position TBD).
I am so glad your accent isn't annoying. Your channel is a joy to view,
Maximum knowledge imparted in a minimum amount of time -- that what Sabine does through her great talent, precision and generosity.
A good lecture for non mathematics types --
Watching this my brain said this to me. A function can appear chaotic because sometimes the function is altering the ocurrence of a property, but sometimes it switches to altering the amplitude of the property. It's like it's flipping between digital to analog and back again.
Can't wait for next week's talk
Differential Equations was a required class for my degree in engineering. Calculus 5 was a prerequisite. Good times.
0:35 That's one of the reasons they are powerful: they allow us to predict, provided the mathematical model correctly describes the physical system. Amazing :)
7:49 Laplace's quote is my favorite quote of all time by anybody.