Hi, I am also trying to get a phd in theoretical physics and when ever I feel down I watch your videos and self motivate myself. Thank you and please continue your work, you're helping many people like myself
@@AndrewDotsonvideos my friend your plots are wrong 18:00 ... ? plug the functions in wolframalpha: integrate 1 * DiracDelta(x-50) + 2 * DiracDelta(x-75) + DiracDelta(x-90)dx
@@alexzan1858 You're asking Wolfram for the plot of the integral, whereas he's just graphing rho on its own. Each of the jumps in the integral corresponds to one of the spikes in rho, with a jump of size equal to the coefficient.
I remember in mechanics we used the normalized 1st moment to find the center of mass of a continuous mass distribution. It made physical sense when I first learned it, but it's fascinating how it comes about in statisstics.
Andrew you are such a good role model for what a physicist should be, and just for how to be a good person. Putting so much effort into sharing your knowledge and the details of your life is truly admirable.
Excited to see more. This might be stretching things in terms of a request, but have you ever studied the generation of gravitational waves? I've heard it involves a "quadrupole moment". If that's something you're familiar with, I'd be interested to see how it fits in with the rest of the content (even if it's just a few sentences tossed in). Don't worry about it too much if not, though. I'll have to sit down and learn it sooner or later.
If I recall, the quadrupole moment for the distribution of mass in a system is hiding its meaning in statistics. You can think of a dipole as being the expected value or a weighted average of the distribution of mass (or charge, the math is the same), and analogously the quadrupole moment would be the covariance of the distribution. Normally, this is represented as a matrix (i.e the covariance matrix). Higher order multipoles like the quadrupole moment or hexadecapole moment in a multipole expansion would be the skewness or kurtosis of the distribution. In gravitational wave emission, the rate of energy loss from gravitational radiation is proportional to the rate of change of the covariance or the quadrupole. I think the reason why it is the quadrupole rather than a dipole like E&M is because the dipole is zero, since mass only comes in one variety while charge comes in two (plus or minus). I’m still a novice grad student tho so someone feel free to correct me
My daughter, a sophomore in high school, is taking Statistics... a subject I never had much interest in, yet always wanted to kind of understand. I now have a better understanding, conceptually, of what goes into Statistics. Thanks, Andrew! I hope you make the third video of this series soon because I'm on to video #2.
Hey Andrew, I wanted to express my gratitude specifically for your teaching style! I often think about how best to explain certain concepts, and I find your pace, motivation, and balance of abstractness and concreteness to be excellent!
Thank you for the video. I'm struggling with understanding the different types of moments in EM and what they all mean. I have exam in it later this month, and this video has made the topic much more intuitive to me. Cheers Andrew!!!
Yeah! Another unique series which is not covered extensively on yt. This is why I love this channel. Thanks Andrew! A request: I am learning tensor calculus through your playlist and I think that it will be very helpful if you do a video on actually solving the Einstein Field Equations for a particular problem. It would be extremely helpful for "new to GR" people like me. Thanks in advance!
@@rikthecuber Your first suggestion might take a while, but the approximation is called the static weak-field limit. It expresses the 00 component of the metric in terms of the gravitational potential, reducing the EFE to Poissons equation!
I don't even know if you'll read this or not but- I started watching your videos about 2-3 years back when I was in 9/10th standard and you inspired me to take up science stream. Giving final Board exams offline (like GCSEs in uk but in India) after 2 years of learning science online this week is super hard and challenging but then whenever I feel like ok that's it I'm so done with this- I come back here to remind myself why I chose these subjects in the first place. With this (I should probably focus on my syllabus lol) thank you for motivating me to work harder again and learn physics. Love from India!
As a highschool student who doesn't take physics this both makes complete sense and no sense at the same time. Regardless I enjoyed the video. (Also btw pretty sure its spelt duhskreehte.)
Hi Andrew, I just want to say that I've been following you since you first started grad school when I was just starting undergrad. Your videos have been really good at motivating me to go for grad school, and just yesterday, I received an offer of admission for a PhD program in physics at my dream school, with scholarship! It seemed super daunting initially but damn does it feel good. Thanks for the good videos
Amazing, enjoyed this vdo so very much. I just finished high school recently although I've been cheating and grabbing undergrad stuff from your channel since the last 2 years😂😂. Can't wait for part 2🎉
Your opening comments remind me of Von Neumann's quip, "You don't understand mathematics, you just get used to it." This might go doubly for physics (certainly QM!!)
Me, a graduate student in theoretical physics : "wtf is a moment, never heard that word before" Is it a thing you study in the US? Here in the UK I've literally never heard of it, apart from maybe moments of inertia from 1st year CM where I just thought it was another word for inertia lol Edit : I guess there's also dipole "moments" in EM but I just thought it was an effective momentum thing from charge lol, we never actually went through what a moment is so kinda intrigued by this video series, keep it up :)
No I’m actually in a similar boat. The word moment wasn’t new of course but in the language of moments of distributions it was completely new for me in grad school. Kinda nice to know I’m not alone 😂
It's probably more common in other languages. At least in German, torque is called "Drehmoment" (moment of rotation), so already in classical mechanics you have to deal with two moments
You know Andrew... I always wondered if I was gonna be any good at TA duties, because I plan on going for a doctorate after completing my Master's. Seeing you explain like this, in a well-structured and easily comprehensible manner, makes me wonder even harder if I'm gonna be any good. 😅 Nice video, by the way. Excited to see whats next.
Look how many one note tabs I have open for this series. This is a pretty fundamental concept and it's still taken dozens and dozens of hours to prepare. Just keep asking yourself questions about what you think you know! Takes time, but always worth it.
Hi, I was wondering if you would go into moment-generating functions at a later part of this series, and discuss situations where a distribution does not have a moment-generating function, such that quantities such as the mean and the variance cannot be defined. Thanks.
I was tempted to use the generating function in this video but thought it would seem I just pulled it out of no where. Maybe it would be helpful, I’ll think about it!
By the same analogy, I guess Quantum Mechanics should be on the same boat as "moments". As in we have developed a new theory, but can we explain it completely to someone? What are your thoughts on this?
i remember studying A level physics (physics qualification before undergrad in uk) years ago and clicking on this video thinking it will be like moment=force*distance rofl.
So you could look at it as a definition, or you can look at representations of the delta function, like as a limit of a Gaussian, and then perform the integral to show that it holds. That could be one way of showing it, but I still think of it as a defintion
Hey 2nd semester of physics here, looking for 2 books, 1 for thermodynamics 1 for lagrange/hamilton's principle. Can someone recommend smth nice? Would be really grateful
Classical Mechanics by Taylor is my go-to for undergrad class mech topics like those you've mentioned. For thermal physics/thermodynamics I currently have Schroeder but I personally think there are still better books that you can keep on scouring for online...
Hey, great video, even on high-school level, but I don't really understand the second property of the delta-distribution. If you multiply any function by the distribution, why do you get the value at that point? Why is it not infinite at this point, because the value of a delta-function is either zero or "infinity", and infinity times any positive number is infinity again. What did I get wrong/overhear? Greetings from Germany!
It’s not that the product gives f(a), the integral does. The delta function is formally infinite at a point, but that region of integration is also infinitesimal, so it’s roughly like infinity*0 integrated gives f(a). Try not to think of it as a function, but as a limit of one.
I really love the tab names "attempt 1" then a few tabs then "attempt 2" then "ok fr this time" and "should have made a skit" lol
Hi, I am also trying to get a phd in theoretical physics and when ever I feel down I watch your videos and self motivate myself. Thank you and please continue your work, you're helping many people like myself
Means a lot, thank you!
@@AndrewDotsonvideos my friend your plots are wrong 18:00 ... ? plug the functions in wolframalpha: integrate 1 * DiracDelta(x-50) + 2 * DiracDelta(x-75) + DiracDelta(x-90)dx
@@alexzan1858 You're asking Wolfram for the plot of the integral, whereas he's just graphing rho on its own. Each of the jumps in the integral corresponds to one of the spikes in rho, with a jump of size equal to the coefficient.
I have a good analogy for a moment: Imagine you have a thing and then you have a distance from it.
Write that down write that down
Charles will be proud :)
certified moment moment
certified funny comment
@@lucasmurcutt6894 certified comment moment
I like how the second to last section in the notes is, "ok fr this time" 😂😂😂
"Ya see its this thing like another thing because of a third thing"
- da best TA ever
I remember in mechanics we used the normalized 1st moment to find the center of mass of a continuous mass distribution.
It made physical sense when I first learned it, but it's fascinating how it comes about in statisstics.
You’ve pointed out the first punchline of the next video:)
Andrew, You are a great teacher. Thank you for doing this for us.
“Integrals waiting to happen”
Well that caught me off guard 😂
Yay new series by _Dr_ Dotson!
Andrew you are such a good role model for what a physicist should be, and just for how to be a good person. Putting so much effort into sharing your knowledge and the details of your life is truly admirable.
108th 😭 ~ Love, Mom ❤
Excited to see more. This might be stretching things in terms of a request, but have you ever studied the generation of gravitational waves? I've heard it involves a "quadrupole moment". If that's something you're familiar with, I'd be interested to see how it fits in with the rest of the content (even if it's just a few sentences tossed in). Don't worry about it too much if not, though. I'll have to sit down and learn it sooner or later.
Radiation from multipoles isn’t something I had thought to talk about (honestly I’d have to learn a lot more I’m sure), definitely gonna look into it!
If I recall, the quadrupole moment for the distribution of mass in a system is hiding its meaning in statistics. You can think of a dipole as being the expected value or a weighted average of the distribution of mass (or charge, the math is the same), and analogously the quadrupole moment would be the covariance of the distribution. Normally, this is represented as a matrix (i.e the covariance matrix). Higher order multipoles like the quadrupole moment or hexadecapole moment in a multipole expansion would be the skewness or kurtosis of the distribution. In gravitational wave emission, the rate of energy loss from gravitational radiation is proportional to the rate of change of the covariance or the quadrupole. I think the reason why it is the quadrupole rather than a dipole like E&M is because the dipole is zero, since mass only comes in one variety while charge comes in two (plus or minus). I’m still a novice grad student tho so someone feel free to correct me
I don't know, but there's a guy on TH-cam who makes videos on General Relativity (and Tensor Calculus too) that are really good, so maybe ask him
@@thecoloroctet1365 name of the channel?
@@apostolismoschopoulos1876way too late, but he might be taking about eigenchris
great shit Andrew, would love to see more videos in this vein
My daughter, a sophomore in high school, is taking Statistics... a subject I never had much interest in, yet always wanted to kind of understand. I now have a better understanding, conceptually, of what goes into Statistics. Thanks, Andrew! I hope you make the third video of this series soon because I'm on to video #2.
i have been waiting for this *moment* for two weeks
Hey Andrew, I wanted to express my gratitude specifically for your teaching style! I often think about how best to explain certain concepts, and I find your pace, motivation, and balance of abstractness and concreteness to be excellent!
I was just looking up moments in physics, this is a literal godsend
🙌🏻🙌🏻
I still hold on to the analogy "There is a thing, but there's a distance from the thing"
Thank you for the video. I'm struggling with understanding the different types of moments in EM and what they all mean. I have exam in it later this month, and this video has made the topic much more intuitive to me.
Cheers Andrew!!!
Great explanation. Looking forward to part 2.
Thank Andrew for taking care of undergrads in the crowd!
You got my bell 🔔 for part 2
Lol, I liked the "50% - that was me" backreference to collab with Papa Flammy :D
Yeah! Another unique series which is not covered extensively on yt. This is why I love this channel. Thanks Andrew!
A request: I am learning tensor calculus through your playlist and I think that it will be very helpful if you do a video on actually solving the Einstein Field Equations for a particular problem. It would be extremely helpful for "new to GR" people like me. Thanks in advance!
Another thing: what approximations do we put in the EFE to get Newton's law of gravitation?
@@rikthecuber Your first suggestion might take a while, but the approximation is called the static weak-field limit. It expresses the 00 component of the metric in terms of the gravitational potential, reducing the EFE to Poissons equation!
I'm only a 1st yr undergrad in the UK, I'll come back to this when I get to this topic 👍🏾
I don't even know if you'll read this or not but- I started watching your videos about 2-3 years back when I was in 9/10th standard and you inspired me to take up science stream. Giving final Board exams offline (like GCSEs in uk but in India) after 2 years of learning science online this week is super hard and challenging but then whenever I feel like ok that's it I'm so done with this- I come back here to remind myself why I chose these subjects in the first place. With this (I should probably focus on my syllabus lol) thank you for motivating me to work harder again and learn physics.
Love from India!
Wow keep it up!
As a highschool student who doesn't take physics this both makes complete sense and no sense at the same time. Regardless I enjoyed the video. (Also btw pretty sure its spelt duhskreehte.)
Terribly sorry for the spelling mistake, reuploading now
I've got a really good analogy for this one - it's like a thing and then there's a distance from it. Hope this clears it up
Hi Andrew, I just want to say that I've been following you since you first started grad school when I was just starting undergrad. Your videos have been really good at motivating me to go for grad school, and just yesterday, I received an offer of admission for a PhD program in physics at my dream school, with scholarship! It seemed super daunting initially but damn does it feel good. Thanks for the good videos
Best instruction to String Theory on TH-cam
Wow, fantastic! Thank you for the diligent explanation…so good.
k
k who?
Congrats for 300k
Amazing, enjoyed this vdo so very much. I just finished high school recently although I've been cheating and grabbing undergrad stuff from your channel since the last 2 years😂😂. Can't wait for part 2🎉
Your opening comments remind me of Von Neumann's quip, "You don't understand mathematics, you just get used to it." This might go doubly for physics (certainly QM!!)
For no reason whatsoever I find incredibly cute the way he says d3r at 8:58 . I can't explain why but I can't stop listening to it! 😂😂
😂
Andrew! It would be awesome to have all 3 parts! The more the better!
Thanks a lot Dr. Andrew for this great video!!!
Very nice Video! looking forward to the next one.
Me, a graduate student in theoretical physics : "wtf is a moment, never heard that word before"
Is it a thing you study in the US? Here in the UK I've literally never heard of it, apart from maybe moments of inertia from 1st year CM where I just thought it was another word for inertia lol
Edit : I guess there's also dipole "moments" in EM but I just thought it was an effective momentum thing from charge lol, we never actually went through what a moment is so kinda intrigued by this video series, keep it up :)
No I’m actually in a similar boat. The word moment wasn’t new of course but in the language of moments of distributions it was completely new for me in grad school. Kinda nice to know I’m not alone 😂
It's probably more common in other languages. At least in German, torque is called "Drehmoment" (moment of rotation), so already in classical mechanics you have to deal with two moments
You know Andrew... I always wondered if I was gonna be any good at TA duties, because I plan on going for a doctorate after completing my Master's. Seeing you explain like this, in a well-structured and easily comprehensible manner, makes me wonder even harder if I'm gonna be any good. 😅
Nice video, by the way. Excited to see whats next.
Look how many one note tabs I have open for this series. This is a pretty fundamental concept and it's still taken dozens and dozens of hours to prepare. Just keep asking yourself questions about what you think you know! Takes time, but always worth it.
ah a video on moments, saved to watch later!
lol jk i'll watch it when i wake up
Hi, I was wondering if you would go into moment-generating functions at a later part of this series, and discuss situations where a distribution does not have a moment-generating function, such that quantities such as the mean and the variance cannot be defined. Thanks.
I was tempted to use the generating function in this video but thought it would seem I just pulled it out of no where. Maybe it would be helpful, I’ll think about it!
I’ve seen the delta function twice. Once in electrostatics and once in quantum mechanics in the context of the generalized uncertainty principle.
Definitely need to talk about magnetic moments
Op iam in class 12 starting but following from class 9
Love strongerer descriptions, in all seriousness.
I've never been this early before
great job man, you are a pretty good educator. really enjoy your content keep it up.
This is nice work you are doing. Please do similar videos on general concepts..
the way he writes a absolutely terrifies me
upd: sorry if that seemed rude, the video is amazing, i just found it funny
Yeah I go for the typed font for “a” but when I write fast it looks atrocious
@@AndrewDotsonvideos i get it haha i also sometimes go for the typed font a but i write it more like alpha
"Punch line" sounds cool... .from now on I am going to do that
More fun to say than summary lol
Very glad I watched this!
I love dirscreeeet data continuity 😄
By the same analogy, I guess Quantum Mechanics should be on the same boat as "moments". As in we have developed a new theory, but can we explain it completely to someone? What are your thoughts on this?
i remember studying A level physics (physics qualification before undergrad in uk) years ago and clicking on this video thinking it will be like moment=force*distance rofl.
25:30
Not only thermodynamics, it's nearly the exact definition of the center of mass.
Yes it’s exactly the center of mass as well;)
At around 6 minutes, does integral=1 follow from the above, or is it also part of the definition?
So you could look at it as a definition, or you can look at representations of the delta function, like as a limit of a Gaussian, and then perform the integral to show that it holds. That could be one way of showing it, but I still think of it as a defintion
Hey
2nd semester of physics here, looking for 2 books, 1 for thermodynamics 1 for lagrange/hamilton's principle.
Can someone recommend smth nice? Would be really grateful
Classical Mechanics by Taylor is my go-to for undergrad class mech topics like those you've mentioned. For thermal physics/thermodynamics I currently have Schroeder but I personally think there are still better books that you can keep on scouring for online...
Pfft! Moments are easy! They're just... like... you have a thing, but... there's a distance from it. Does that clear things up?
Ma bro ❤
Hey, great video, even on high-school level, but I don't really understand the second property of the delta-distribution. If you multiply any function by the distribution, why do you get the value at that point? Why is it not infinite at this point, because the value of a delta-function is either zero or "infinity", and infinity times any positive number is infinity again. What did I get wrong/overhear?
Greetings from Germany!
It’s not that the product gives f(a), the integral does. The delta function is formally infinite at a point, but that region of integration is also infinitesimal, so it’s roughly like infinity*0 integrated gives f(a). Try not to think of it as a function, but as a limit of one.
Lets goooooo
Integrating a delta function is the adult version of telling a kid that 69420x420x69x0x42069 = 0
Isn't that just
imagine there is a thing, and there is the distance from that thing
I was today years old when I realized that I've been spelling dirscreeeet wrong the whole time.
Damn you look young today
0:05 I feel like there can be a lot of this in mathematics. 🙁
Hi do you still learning string theory?
We won't be talking about higher moments...
Sad Friedrich Keller Noises :'(
Definitely open to suggestions but just wasn’t planning on really talking about more than 2nd-3rd order moments
Bruh I have no idea why I am here, I got a C in contemporary math in college 🤣
meanwhile me, a high schooler expecting you to talk about mr^2 smh
We’ll get there!
You couldn't explained the delta function more clearly if you started by the rect function
discrete*
Wow this video is incredible! Nice job! Also, I'm the 69th comment
nice
Nice
6:48 Hello? Where's the dx? You've committed a sin!
First
youre getting grey
I’m doing a PhD in biochemistry so god knows what I’m doing here…
I am god and i dont know
Which whiteboard software are you using in this video?
Gaomon pd200, software is just one note