I had a similar experience with one of my teachers. He said "just look at the units and think about what it should be". 90% of students don't understand it, but for the 10% that do, it is a powerful tool.
It gets way more confusing as an American when you don't know which numbers are in standard which ones are metric because it's seldom specified..., It might be intuitive which ones are length, Mass, time electrical etc, but then start mixing moles per oz and decameters² and neither is specified and you got to figure it out... no fun.
Fantastic video! DA is something that I practiced extensively through my freshman and sophomore classes and it helped so much with basic sanity checks. Unfortunately, through the second half of my sophomore year and my junior year, I never thought about DA analysis again outside of basic unit conversations. Thank you for reminding me of this. I got caught up in the “memorize everything” mentality and this was a good reminder to change how I think of my course work for my senior year :)
I know you said something about 3B1B influencing you to create more videos, but I would urge you to do it despite the initial reason. His videos can be very hard to grasp for people like me who don't have a strong foundation to experiment with further in their mind (same for the PBS spacetime guy, he got very intense over the years). Your few videos have made me more excited to tackle the complex nature of mathematics and chemistry, and the simplistic explanations and friendly disposition do wonders for my cognitive retention. Thank you for your time so far, and I hope you do well no matter what you choose to do!
IMO it's natural to always divide x^n by n!, because if you construct polynomials by repeatedly integrating, you get 1/1, x/1, x^2/2, x^3/6, x^4/24 ..., x^n/n! so if you see x^n, think n!/n! x^n
Fahrenheit and Celsius are 2 buildings next to each other. Celsius is on a hill that's as tall as Fahrenheit's 32nd floor. There are 9 floors in Fahrenheit for every 5 floors in Celsius, and they have a weird shared basement that goes down forever. You're on the 20th floor of Celsius, looking at Fahrenheit. Which floor are you directly across from? (The 68th.)
I ask my trusty navigator google and it does the heavy lifting It’s quite interesting that both Celsius and Fahrenheit are equally bad as units. Both are only used to calculate differences in temperatures, whereas Kelvin starts from zero like every other unit.
@@mindmaster107 Celsius is just Kelvin shifted to mark the phase shifts of water, which tend to be quite important on Earth, making it clearly the less equally bad unit
@@mindmaster107 yes, and there was an example estimating the order of magnitude of the Planck time with dimensional analysis. on other thing that was very memorable is the derivation of Schrodinger's from the principle of least action (I believe) with calculus of variations. My notes are no longer available and I can't find that anywhere else
@@mindmaster107 my teachers covered this in GCSE but then didn't reinforce it. It was taught almost as a curiosity so we never used it. It was only in my second year of an astrophys degree that my tutor pushed this hard and its use was embedded. My son is now beginning his GCSE period. Guess what I'm covering with him today :)
I am confused as to when the exponential to a dimension is 1. Also great video it made me change my perspective on some of the aspects of problem solving.
Think about it this way: You cannot add quantities that are attached to different dimensions; you cannot a length to a temperature or an intensity. Now, for instance, consider what would happen if you i.e. took the exponential of one metre. By its Taylor series, we know that e^(1m) would be 1 + 1m + 1m²/2 + 1m³/6 + ... + 1m^k/k! + ... You would be adding lengths to areas, volumes, and even worse, a dimensionless number! So this means there is no such thing as the exponential of a length. You can generalise this example to include everything that is not dimensionless, and thus you can also show no function that is not a monomial (i.e. of the form x^k) can ever take a dimensional argument.
I just started physics at school so this is perfect timing! I have a question, what if a formula involves addition? Like v = u + at. I suppose such a simple formula needs no derivation
lol yea i will derive equations mid exam no problem.... except my professor want us to memorize the equations because he's gonna reduce the exam time so we won't have time to derive shit. i'm talking about the equations for the transistors btw. yea all of them are just a form of Kirchhoff law and you can see how they differ but there's too much of them and little to no difference
Nothing beats the speed of memorising everything, but memory can only take you so far before the equations count upwards to the hundreds. (I plan to make a video on exam technique, so don’t worry about that) Also, I think the real fun of physics is finding new things, and not showing how equations are even theorised feels like only showing of magic tricks for 13 years without teaching how even one of them are actually done.
I would suggest that in your studies, you spend some time deriving the equations themselves. Understanding where they come from and how they work will make recall easier on the exam. Also just practice lots of problems until it feels like riding a bike.
@@Wagon_Lord oh I already do that, there's just no way I would be memorizing them It even says in the book how to "memorize" them like how there's a factor of (1+B)Re in the denominator of the emitter bias which makes sense as we have a resistor on the emitter now. It's just he was really ridiculous saying "just memorize lol" while he could have taught us the "intuition"
What are you going to do about constants, like you cant tell anything about constants if there is any one at all, this is the only drawback and it renders it useless. I prefer deriving all of my equations, like first you think it's going to take forever but doing such enough times you can see patterns, like equations are talking to you. My interest is in Mathematics but it doesn't hurt to do some Physics every once in a while.😊
Dimensional analysis is often used as the first round in theoretical research, as it just narrows down possible answers to look for. It doesn’t always help, but hopefully as one of the many tools you wield, it should help especially in fields you are unfamiliar in.
? It's grade a 11 concept? Although I didn't gave much importance to it somehow just cuz in jee exam preparation you use formulas to many times it just gets fixed😅😅🤣
The most chill video of all
I love this bear explaining physics that have nothing to do with my studies. New fave channel ❤
I just found your channel, I can't believe how amazing it is for every physics liver 💞😭😭😭
I had a similar experience with one of my teachers. He said "just look at the units and think about what it should be". 90% of students don't understand it, but for the 10% that do, it is a powerful tool.
This is why I’m making videos ;)
It gets way more confusing as an American when you don't know which numbers are in standard which ones are metric because it's seldom specified..., It might be intuitive which ones are length, Mass, time electrical etc, but then start mixing moles per oz and decameters² and neither is specified and you got to figure it out... no fun.
Fantastic video! DA is something that I practiced extensively through my freshman and sophomore classes and it helped so much with basic sanity checks. Unfortunately, through the second half of my sophomore year and my junior year, I never thought about DA analysis again outside of basic unit conversations. Thank you for reminding me of this. I got caught up in the “memorize everything” mentality and this was a good reminder to change how I think of my course work for my senior year :)
I know you said something about 3B1B influencing you to create more videos, but I would urge you to do it despite the initial reason. His videos can be very hard to grasp for people like me who don't have a strong foundation to experiment with further in their mind (same for the PBS spacetime guy, he got very intense over the years). Your few videos have made me more excited to tackle the complex nature of mathematics and chemistry, and the simplistic explanations and friendly disposition do wonders for my cognitive retention. Thank you for your time so far, and I hope you do well no matter what you choose to do!
IMO it's natural to always divide x^n by n!, because if you construct polynomials by repeatedly integrating, you get 1/1, x/1, x^2/2, x^3/6, x^4/24 ..., x^n/n!
so if you see x^n, think n!/n! x^n
The magic of Taylor expansion :D
Such underrated channel
You should do more videos on this subject. it is interesting.
How good! I'm searching for the same thing and you just uploaded a video! Thank you so much!!
Reynolds later went on to commercial success in the field of aluminum foil.
Thank you for this, very good. I'm still graduating, but I very much will pursue a PHD
This was a beautiful video. Thank you!
My friend at high school excelled at this technique intuitively and it always amazed me. He's now studying engineering btw
if only there was something like this for finding quotes from Macbeth during the paper haha
Fahrenheit and Celsius are 2 buildings next to each other. Celsius is on a hill that's as tall as Fahrenheit's 32nd floor. There are 9 floors in Fahrenheit for every 5 floors in Celsius, and they have a weird shared basement that goes down forever. You're on the 20th floor of Celsius, looking at Fahrenheit. Which floor are you directly across from? (The 68th.)
I ask my trusty navigator google and it does the heavy lifting
It’s quite interesting that both Celsius and Fahrenheit are equally bad as units. Both are only used to calculate differences in temperatures, whereas Kelvin starts from zero like every other unit.
@@mindmaster107 Celsius is just Kelvin shifted to mark the phase shifts of water, which tend to be quite important on Earth, making it clearly the less equally bad unit
this was literally the first thing they taught us in uni physics
Would be nice if they taught it a little earlier :P
@@mindmaster107 lol they teach this in 11th class in India
Thats good :D
@@mindmaster107 yes, and there was an example estimating the order of magnitude of the Planck time with dimensional analysis. on other thing that was very memorable is the derivation of Schrodinger's from the principle of least action (I believe) with calculus of variations. My notes are no longer available and I can't find that anywhere else
@@mindmaster107 my teachers covered this in GCSE but then didn't reinforce it. It was taught almost as a curiosity so we never used it. It was only in my second year of an astrophys degree that my tutor pushed this hard and its use was embedded.
My son is now beginning his GCSE period. Guess what I'm covering with him today :)
I really do relate to that chipmunk when he shows his head gonna explode ... It is really funny
I am confused as to when the exponential to a dimension is 1. Also great video it made me change my perspective on some of the aspects of problem solving.
Think about it this way: You cannot add quantities that are attached to different dimensions; you cannot a length to a temperature or an intensity. Now, for instance, consider what would happen if you i.e. took the exponential of one metre. By its Taylor series, we know that e^(1m) would be 1 + 1m + 1m²/2 + 1m³/6 + ... + 1m^k/k! + ... You would be adding lengths to areas, volumes, and even worse, a dimensionless number! So this means there is no such thing as the exponential of a length. You can generalise this example to include everything that is not dimensionless, and thus you can also show no function that is not a monomial (i.e. of the form x^k) can ever take a dimensional argument.
In here Dimensional Analysis is taught before college level and yes it's very very very useful!!!!
I’m in love with your videos 😌
Bro this is on Khan Academy. That is pretty crazy. Thanks for the notice!
It’s not a secret, since most people who are good at physics can do it.
I’m just annoyed at how little emphasis is placed on it.
nice
When you said “Honey, air, water”, I expected some sort of Avatar intro 😂
Everything changed when the plasma nation attacked
Yes, but what if we forget or mix up units? (Like for example at 6:40 where g should be in ms^-2.😊)
I get sent to the embarrassing dimension. o////o
I hate furries but you're an exception❤
It's the bear guy again. Nice video.
I like this channel
Dimensional analysis isn't taught until PhD level? Since when? O.o It was in my high school curriculum.
It is usually taught at undergraduate level, for first years.
But yeah, still too late lol
I just started physics at school so this is perfect timing! I have a question, what if a formula involves addition? Like v = u + at. I suppose such a simple formula needs no derivation
If two terms are being added, they must have the same units. v is ms^-1 and a is ms^-2, so at is ms^-1.
@@mindmaster107 ohhh yeah, that makes sense
babe wake up, a new physics video from the funny anthropomorphic bear just dropped 😎
I woke up to a very funny message in my comment section XD
Thanks for commenting!
do you have a discord server or somewhere where we can ask you questions?
Comments, lol
Did the title of this video change?
Btw haven’t watched yet, Will later when I get a chance
Yes. I’m not very good at naming things first try
lol yea i will derive equations mid exam no problem....
except my professor want us to memorize the equations because he's gonna reduce the exam time so we won't have time to derive shit. i'm talking about the equations for the transistors btw. yea all of them are just a form of Kirchhoff law and you can see how they differ but there's too much of them and little to no difference
Nothing beats the speed of memorising everything, but memory can only take you so far before the equations count upwards to the hundreds. (I plan to make a video on exam technique, so don’t worry about that)
Also, I think the real fun of physics is finding new things, and not showing how equations are even theorised feels like only showing of magic tricks for 13 years without teaching how even one of them are actually done.
I would suggest that in your studies, you spend some time deriving the equations themselves. Understanding where they come from and how they work will make recall easier on the exam. Also just practice lots of problems until it feels like riding a bike.
@@Wagon_Lord oh I already do that, there's just no way I would be memorizing them
It even says in the book how to "memorize" them like how there's a factor of (1+B)Re in the denominator of the emitter bias which makes sense as we have a resistor on the emitter now.
It's just he was really ridiculous saying "just memorize lol" while he could have taught us the "intuition"
i think there is an error in 6:43.... g=10ms^-2 not ms^-1
Whoops. Thanks for the catch.
👍👍👍
What are you going to do about constants, like you cant tell anything about constants if there is any one at all, this is the only drawback and it renders it useless. I prefer deriving all of my equations, like first you think it's going to take forever but doing such enough times you can see patterns, like equations are talking to you. My interest is in Mathematics but it doesn't hurt to do some Physics every once in a while.😊
Dimensional analysis is often used as the first round in theoretical research, as it just narrows down possible answers to look for.
It doesn’t always help, but hopefully as one of the many tools you wield, it should help especially in fields you are unfamiliar in.
Dimensional analysis is begging for a programmatic approach. Imagine algorithmic lists of these types of numbers.
? It's grade a 11 concept? Although I didn't gave much importance to it somehow just cuz in jee exam preparation you use formulas to many times it just gets fixed😅😅🤣
Great you got taught it early lol
From many people I’ve talked to, its somehow not taught until university