I've taught this to my students for yrs. Always surprised me that so few other profs bother teaching it as it is incredibly powerful. One of my students actually used it in biology research to study tree rings actually (literal application of logs to logs, heh).
I would if basic algebra weren't already pushing the limit of what my (college) students can do. And for my population (students who immediately want to say all increasing graphs share the same relationship regardless of the shape of the line), I personally like the additional level of thinking that comes from linearization, even if it is less precise than log-log plots. If all I cared about was them getting the equation they could just take a power regression and that would be that. Asking them to linearize forces them to actually consider the shape of the graph and try different possibilities rather than just running it through some algorithm they don't understand which just spits out an answer. In my situation, the tradeoff between power and conceptual clarity isn't worth it, especially in an introductory physics course where every relationship we test will either be proportional, quadratic, inverse, inverse-square, or square-root. But if my students were higher level or would actually be doing research in the future then this would definitely be a worthwhile skill to have in their toolkits.
@@SirPhysics I always use the power law regression approach when I can to develop the formulas empirically and then we discuss the conceptual underpinings and develop intuitions from proportional reasoning exercises. That also typically follows the historical route which I like since I can frame the lab activities as if students are discovering something new on their own, and then I can come in with a theorist's background to find conceptual structure to those formulas and we can outline assumptions etc. I def feel ya when it comes to algebra standing in the way of things, but otoh even if you had a linear relationship they won't be able to all grasp how regression works either. I'm actually slowly working on ways to develop approaches that dramatically reduce reliance on algebra itself in my low level courses, instead aiming to have students find graphical solns instead. I really want to highlight how straight algebra is just one tool that they can use to solve problems but sometimes other tools can be more effective/efficient/reliable.
@@techedzee Yeah for sure they are doing their best Whoopie impression, lol. I think this is one of those things where you almost have to maybe do it yourself and get comfy with the blind utility of it first before ya can appreciate the algebra for how/why it works too. Preparing the math with log operations isn't all that alien but graphing log A vs log B or whatever is what rly throws students for a loop I bet. The upshot is even if they don't grasp all of its nuance, it is still potentially hugely empowering to be able to find a bunch of natural relationships using this approach. I've had a student use it to compare diameters of tree trunks to the age of a tree. I use it for loads of stuff in E&M too now.
@@jacobmartin8332you weren't / aren't ready. for this obviously. I don't know, I think you should absolutely trust everything to a random youtuber versus your teacher.
@@jacobmartin8332 Just plot whatever graph they are told to and not think about it lol. If you are told the relationship is y=kx^2 you will just plot y against x^2 a lot of the time because you know the relationship already. But this technique is useful where you don't know the relationship.
I know that the UK education system has been through some changes recently, but this used to be standard teaching for physics A-Level in the 1960s. In fact we were issued with log-log graph paper for our A-Level physics practical exam. We had to plot our experimental results on it and derive an equation from the resulting (more-or-less) straight line result. I am surprised that it’s not still taught in schools!
yeah, same, my parents (and one of physics teacher - the old one) also mentioned that log tables were taught and such. I am not that old, but i appreciate good things and so i always wonder why such good things were removed from edu sys.
This one caught me out in first year labs. A good thing to remember is that if you are actually trying to validate a theory you should be tracking the errors of your data (as any good experimentalist would) which means that plotting a linear regression log-log graph isn't actually statistically accurate, although it's still pretty good, since you no longer have gaussian error distributions on your data.
Yes, the variation of error along the plot makes the accuracy of the linear regression analysis dubious. Also, in practice it is extremely difficult to apportion your experimental points such that your log-log graph does not consist of a bunch of points clustered at one end of the plot, and one lone point at the other end.
Taking logarithms also works nicely for an exponential relationship, y = Ae^(kx), where A and k are some constants (note that this works for any base b, but assuming b > 0, b^a = e^(a ln(b)), so we'll stick to e as a base). Then ln y = ln A + kx, so we can plot ln y against x to get a straight line relationship.
Hey everyone, thanks for watching this video! If you enjoyed it, please feel free to subscribe, and check out my "Equations Explained" playlist here: th-cam.com/play/PLOlz9q28K2e5j4UHkeBXhrtga_qC5ZCzf.html Edit: By the way, the title is just a little joke, parodying the "Experts HATE this guy for ___" videos. Thanks for your support!
@Parth G Hey, parth it's has been a long time since the last astronomy video. SUGGESTION: the relative motion of the center of masses of the earth-moon system to the earth-sun system,
Happy you are teaching these concepts. As we get away from graphical paper and pencil learning we've lost the feel for curve fitting and now with computers this is so much more important than ever (they can't read graph paper as my professors use to say).
This is a really cool application of logs. I just learned about them this year and it's cool to know some of the tricks one can use to verify experimental results. Thanks for the video.👍
Another great video, Parth. I think the experimential math methods you've shown in this video were excellent. Math methods in experimental physics isn't explained much from what I've seen on youtube but they are good to know especially for a theoretical physicist. Keep it up. I wonder if there are math tricks to figuring out experimental data revolving around a sine or cosine wave.
Note at 6:53 Linear regression minimizes the average squared distance between each point and the line rather than the average distance between points and the line as is shown in the video. EDIT: I see someone else already mentioned this and Parth responded it's intentional.
It would be great to see a part 2 of this video which deals with dimensional analysis and thus showing that for many laws in physics we are able to identify the proportionality simply by looking at the units/dimensions of the relevant variables and furthermore are able to find variables which are not relevant for the problem, e.g. the frequency of a string pendulum being not dependent on the mass which might be confusing on first sight.
We civil Engineerings often plot log-log plot or semi log plots rather than arithmetic plots. I found the reason now!! Connected all the points 🦋Excellent 🙌😍
Hi, Parth! Nice video. A nice continuation to it would be to highlight how log-scale linearization distorts the error distribution of the fitted parameters. Keep up the good work
Very nice trick and definitely useful for checking if there is a power law relationship in your data. However, a small problem with this approach is random errors in the measurements. When you take the logarithm of your measured B values, it can be thought that the logarithm actually operates on B + v where B is the 'true' values and v is a random measurement error. Then, when you do linear regression to estimate the parameters theta and r, the random error may cause your estimated parameters to be biased to some direction. To avoid the bias you could use nonlinear regression to estimate these parameters directly without taking the logarithm, but this makes the math a bit more difficult.
This is great! I wasn't aware of this. Thank you One minor nitpicking point. While linear regression in the "log" space is a great start, I think you eventually want to do regression (non-linear) in the original space. doing regression in the log space is min (log(y) - (log(beta) + alpha*log(x)))^2 = min (log(y/(beta*x^alpha)))^2, which, as desired, has its minimum when the prediction and the target are equal, but under predictions are weighted more than over predictions, due to the asymmetry of log. For the best fit, I think you eventually want to solve for alpha and beta in the original space "min (y - beta*x^alpha)^2". I could be wrong on this.
A neat trick, this! The close relationship of logarithms to information comes to mind, which may show up here as how much storage -- how much complexity -- is required to massage the raw data into a log-log linear form. That's interesting by itself, but it gets "a bit" more interesting if one considers that it is the *lack* of information that most sharply defines the transition from classical-causal to quantum-indefinite physics.
Let there be light! Thanks! Used a long hand version of this to arrive at the relationship when those constants and power terms don't match a predicted value! Need to take maths seriously for all these easy tricks to make that task easier.
First, the common logarithm (base 10) is usually used for log/log plots and log/log graphing paper is ruled in base 10 decades. Second, physicists use chi squared fits rather than linear regression such that data points that are well-known are weighted more heavily. Third, statistical and experimental fluctuations limit the knowledge gained by fitting data to a parametrized model. The graph shown is unlikely to have better than 1-2% tolerances in slope and intercept.
Computer science people know this trick pretty universally when they're crunching data. Following chats on projects that are a little over my head, I hear "the graph is log/log, right?" or some variation all the time. Nice to see the y=mx+b(in the US) relationship: now it makes total sense.
I hope you know you're a hero to young physicists who yearn to explore their independent minds to think intuitively and diligently. You are the reason why my love for science has amplified. I'm contented that I found you're channel on youtube for inspiration. I hope I become a great physicist, and when I do, I'll make sure to credit your name for all the help you have given me. Thank You, friend.
This is something you learn to do in any good collegiate introduction to statistics course. This was done in my AP Stats course, where we were given a graph that was obviously not linear but plotting it using the logarithm (base 10, which should change nothing) of the two variables makes our plots linear. This better helps us find the log(x_hat) and therefore our x_hat. It was a very nice trick and one I never realized was used so often.
I love this channel, I have watched the video about Lagrangian Mechanics and this one. You have an amazing way to explain and simplify stuff. Looking forward to new videos.
Clever i have to say.thats why i used to love physics in high school. Physics is nothing but using clever tricks to derive expressions for physical phenomenons. I love playing with equations . I remeber understanding calculas by using infinitesimally small change as the trick to integrate for irregular quantities like rotational inertia of a npn uniform body.
It would be nice to show also to people how to deal with interval of uncertainty of measurement after logarithmic transformation. How it modifies Gaussian curve. And overall how to count final interval for constants.
At least with pure wave functions (sines and cosines) you can take a complex log and beget the proportionality constant and power. In this case the power is analogous to the frequency and the proportionality is analogous to the amplitude. Phase shift would be a shift like f(x+a) analogous to a different start date. Then a linearization of these waves would be an absolute value function that oscillates between 2 y values a distance of 2A away from each other. This also leads to more exotic averages. The geometric mean is an exponentiation of the arithmetic mean so graphing it on a logarithmic scale would look easily similar to the arithmetic mean.
Excellent presentation, clear and concise. The way it was presented to me as I started my research: "The power law is very forgiving." It gets a bit hairy when you're trying to show the power law exponent is different to unity.
Brilliant trick. I agree that plotting straight lines is superior as they easily compare with other straight lines. In telecom, we go as far as to use a double Log axis when plotting bit error rate vs power (in dBm).
@@siddharth5339 Not really! Although this is a basic mathematical concept, what you said isn't true. Indian schools mostly make the students rote-learn all the formulae and short-cuts to find the answer by substitution. Or else, they make the students rote-learn high level definitions and understanding of concepts. Ask any Indian high school or even a college kid some questions related to application or basic implementation of these concepts and we'll completely draw a blank. We can also see this in all of those TH-cam videos where Indians are explaining science or engineering concepts - they're just repeating exactly what you'll find in a text book already.
So crazy - thought I was up and running with things for years, looks like there are always new tricks to put them in my bag of tricks... so obvious about taking log only after watching this tricky-maths video.
One more thing to add: The exponent is by definition dimensionless, and since the equations of physically measured variables require units to be consistent on each side, it is extremely unlikely for the exponent to be anything other than an integer or half integer. After all, the a distance measured in meters raised to the 2.0249th power means the coefficient has some *awfully* heavy lifting to do in order to help such a strange denomination of meters conspire to equate to Newtons on the other side (or whatever the units work out in a given relationship). This fact lets you round the exponents and see the deviation as something hidden in your experimental setup or measurement techniques.
Nice video! I just want to add that even polynomial laws don't have straight line log-log plots, even lines! So if you have a law where y = ax + b for example, the log-log plot will be curved. For lines and parabolas, you can use translations to straighten out the plot, but there's nothing that can be done for cubic polynomials and above. I think a lot of people confuse power laws and polynomials laws, since the former is a subset of the latter, but in this case it's an important distinction to be made.
I would use gradient of the line in direction of perpendicular line. We can find three different reasons for that. One reason is that it is geometrically dual vector (also Hodge dual to movement vectors on line) and line elements are created by points on tangent space starting at some point of the line. The Hodge dual in 2D to any vector in direction of the line is again a vector and it coincides with normal vector of the line. And normal vector of the line is its gradient.
The reasons for that: 1) inner product or duality 2) analytical geometry, how equation of the line is constructed in a point way (dual construction to its vector way) 3) differential geometry - gradient is perpendicular to contour line at given point 4) symmetry - gradient splits equally the curve at some point
in some what related manner, I feel like this how deep neural network works, essentially try to take real life highly non-linear data, and gradually reduce the dimensionality and try to more "linear-ize" in each layer, until you get to the final layer which output an approximate linear function that correlate real life data to some derived parameters.
I used to tell my students that everything we plot in Physics is going to give us a line, even if we think it should be a curve. They looked at me like I just landed in a spaceship from Mars because we had just looked at several common relationships (y =kx, y =kx^2, y = k/x, etc.) and the curves they generate. 6:24 for some strange reason in the United States we use b instead of c for the y-intercept. using c makes more sense to me, but we are stuck with b.
Excellent explanation and very nice visuals. I almost didn't watch this though, because I was put off by the title! There is so much click bait on TH-cam that uses these over-the-top, all-caps HATES! phrases, that I wonder if you shouldn't perhaps consider using something more in keeping with your content? Again, the content is wonderful, just a comment on the title.
Great tip thanks! The only thing I would mention is that the diode plot is only curved for very low voltages. After that (beyond the bias voltage) it’s nice and straight.
Good Info..I had tried plotting a curve by curve fitting...and did some guesswork to find constant and power. but this plotting log-log graph is good. Now I understand importance of semilog paper
My goodness I used this all the time in my physics lab in +1 & +2 but never thought about why are logarithms being used here!! Thank you so much Parth this was amazing 🤩🤩
The only problem is that you have to be careful about the propagation of incertitude (error bars) ! :) So this method will not produce good results if you don't have error associated to your data. Also non-linear regression are not so hard to do with good programs like ROOT
Wonderfully Explained.. In Indian Carnatic music.. there's a way word for "Explaining or Expressing things in simpler way".. The word, " KAKAPADAM" mean... " As easy as peeling out banana.".. This Suits Parth's Way of Physics 😊
As a former professional biotechnical analist I completely relate to this and want to add: by using a linear progression analysis you can give real estimates of the confidence of your data if you have enough measurements.
Awesome!! Thank you for providing this wonderful and useful explanation of logarithms. But, speaking of physics, most of the quantities have unit. Is it okay to directly put logarithms on those quantities? Let's say, the length of a rope is 1 m which equals to 100 cm; however Log(1 m) doesn't equal to Log(100 cm). I really get confused, cuz I've seen lot of quantities that are under logarithms symbol by many physicists.
That's a really interesting question!! Apparently from what I found, the logarithm can only be taken of a dimensionless (no unit) quantity, and thus when applying it to a quantity with units one is actually finding the logarithm of the quantity as if it were dimensionless. So something like log(18 s) cannot be treated rigorously but is instead moreso a shorthand for log(18 s / 1 s) = log(18). I believe that the reason this still can be applied to relationships between physical quantities is because such relationships hold true regardless of units: for example, F=ma is not an equation with units, but instead one that requires all of the units to "agree" with each other for it to provide any meaningful information. Main reference for the first part is math.stackexchange.com/questions/238390/units-of-a-log-of-a-physical-quantity, they link a very interesting journal article that's worth a read.
There are real problems with using this routine rather than employing a good, weighted, nonlinear regression routine. One obvious problem is that routines employing ln(data) improperly suppress the larger standard deviations. Another problem is that one often should use the result when the independent variable is 0, which cannot be done with ln(data).
I am wondering why most teachers (or at least the ones I know) most of the time make things much harder than they really are. Than you @Parth G for your videos.
I've taught this to my students for yrs. Always surprised me that so few other profs bother teaching it as it is incredibly powerful. One of my students actually used it in biology research to study tree rings actually (literal application of logs to logs, heh).
I would if basic algebra weren't already pushing the limit of what my (college) students can do. And for my population (students who immediately want to say all increasing graphs share the same relationship regardless of the shape of the line), I personally like the additional level of thinking that comes from linearization, even if it is less precise than log-log plots. If all I cared about was them getting the equation they could just take a power regression and that would be that. Asking them to linearize forces them to actually consider the shape of the graph and try different possibilities rather than just running it through some algorithm they don't understand which just spits out an answer. In my situation, the tradeoff between power and conceptual clarity isn't worth it, especially in an introductory physics course where every relationship we test will either be proportional, quadratic, inverse, inverse-square, or square-root.
But if my students were higher level or would actually be doing research in the future then this would definitely be a worthwhile skill to have in their toolkits.
@@SirPhysics I always use the power law regression approach when I can to develop the formulas empirically and then we discuss the conceptual underpinings and develop intuitions from proportional reasoning exercises. That also typically follows the historical route which I like since I can frame the lab activities as if students are discovering something new on their own, and then I can come in with a theorist's background to find conceptual structure to those formulas and we can outline assumptions etc.
I def feel ya when it comes to algebra standing in the way of things, but otoh even if you had a linear relationship they won't be able to all grasp how regression works either.
I'm actually slowly working on ways to develop approaches that dramatically reduce reliance on algebra itself in my low level courses, instead aiming to have students find graphical solns instead. I really want to highlight how straight algebra is just one tool that they can use to solve problems but sometimes other tools can be more effective/efficient/reliable.
I was taught all the concepts here but the light 💡 bulb never lit 🔥 up until watching this video. Am sure some of your students are like, “OKAY”
@@techedzee Yeah for sure they are doing their best Whoopie impression, lol. I think this is one of those things where you almost have to maybe do it yourself and get comfy with the blind utility of it first before ya can appreciate the algebra for how/why it works too. Preparing the math with log operations isn't all that alien but graphing log A vs log B or whatever is what rly throws students for a loop I bet.
The upshot is even if they don't grasp all of its nuance, it is still potentially hugely empowering to be able to find a bunch of natural relationships using this approach. I've had a student use it to compare diameters of tree trunks to the age of a tree. I use it for loads of stuff in E&M too now.
Elites are not the elite if everyone is taught the same skills and knowledge....
Damn, I’m surprised my physics teacher never taught us this. This strategy is pretty slick, I like it.
What do people generally do to verify results without such a method?
@@jacobmartin8332you weren't / aren't ready. for this obviously. I don't know, I think you should absolutely trust everything to a random youtuber versus your teacher.
@@jacobmartin8332 Just plot whatever graph they are told to and not think about it lol. If you are told the relationship is y=kx^2 you will just plot y against x^2 a lot of the time because you know the relationship already. But this technique is useful where you don't know the relationship.
Yo, i only learned this in Experimental Physics.
yea :3 sadly the education system dip shit and we have to find an better solution to grow our knowledge. school loans suck.
I know that the UK education system has been through some changes recently, but this used to be standard teaching for physics A-Level in the 1960s. In fact we were issued with log-log graph paper for our A-Level physics practical exam. We had to plot our experimental results on it and derive an equation from the resulting (more-or-less) straight line result. I am surprised that it’s not still taught in schools!
yeah, same, my parents (and one of physics teacher - the old one) also mentioned that log tables were taught and such. I am not that old, but i appreciate good things and so i always wonder why such good things were removed from edu sys.
WOW!! Finally, a simple enough explanation to why most experiment measures go into logarithms!!
Just learned this in my physics course! Blew my mind when I was able to get the correct formula for a bifilar pendulum
niiice
This one caught me out in first year labs. A good thing to remember is that if you are actually trying to validate a theory you should be tracking the errors of your data (as any good experimentalist would) which means that plotting a linear regression log-log graph isn't actually statistically accurate, although it's still pretty good, since you no longer have gaussian error distributions on your data.
I was looking for someone to point that out! 👌
Yes, the variation of error along the plot makes the accuracy of the linear regression analysis dubious. Also, in practice it is extremely difficult to apportion your experimental points such that your log-log graph does not consist of a bunch of points clustered at one end of the plot, and one lone point at the other end.
Well, that's that. Now I know what usually happens in my lab reports. Was a mystery solved today. Thankyou Parth G!
Taking logarithms also works nicely for an exponential relationship, y = Ae^(kx), where A and k are some constants (note that this works for any base b, but assuming b > 0, b^a = e^(a ln(b)), so we'll stick to e as a base).
Then ln y = ln A + kx,
so we can plot ln y against x to get a straight line relationship.
Hey everyone, thanks for watching this video! If you enjoyed it, please feel free to subscribe, and check out my "Equations Explained" playlist here: th-cam.com/play/PLOlz9q28K2e5j4UHkeBXhrtga_qC5ZCzf.html
Edit: By the way, the title is just a little joke, parodying the "Experts HATE this guy for ___" videos. Thanks for your support!
I HAVE LITERALLY WATCHED EVERY VIDEO THRICE!!
@@dhanashrikulkarni5878 me too buddy
Thanks very much for the support guys!
@Parth G Hey, parth it's has been a long time since the last astronomy video. SUGGESTION: the relative motion of the center of masses of the earth-moon system to the earth-sun system,
Happy you are teaching these concepts. As we get away from graphical paper and pencil learning we've lost the feel for curve fitting and now with computers this is so much more important than ever (they can't read graph paper as my professors use to say).
I like how I try to understand these things for fun.
Nice...
Same :D
dont we all?
Same
r/iamverysmart
This was great. Thx Parth! Well presented.
This is a really cool application of logs. I just learned about them this year and it's cool to know some of the tricks one can use to verify experimental results. Thanks for the video.👍
So THAT’s why they love to use Logs for graphs!! Thank you for the awesome explanation!
Love the video. This trick saved me so much pain in so many experiments in undergrad
I know the mechanics behind all of this very well, but it still blows my mind to see it in action. Logs are freaking rad.
Another great video, Parth. I think the experimential math methods you've shown in this video were excellent. Math methods in experimental physics isn't explained much from what I've seen on youtube but they are good to know especially for a theoretical physicist. Keep it up. I wonder if there are math tricks to figuring out experimental data revolving around a sine or cosine wave.
I remember being shown this in Freshman Physics, back in the 20th Century.
Nice presentation!
Note at 6:53
Linear regression minimizes the average squared distance between each point and the line rather than the average distance between points and the line as is shown in the video.
EDIT: I see someone else already mentioned this and Parth responded it's intentional.
Nice! As a physics student, this is something I will send to people when being asked about what I do when doing experiment. Great video!
It would be great to see a part 2 of this video which deals with dimensional analysis and thus showing that for many laws in physics we are able to identify the proportionality simply by looking at the units/dimensions of the relevant variables and furthermore are able to find variables which are not relevant for the problem, e.g. the frequency of a string pendulum being not dependent on the mass which might be confusing on first sight.
We civil Engineerings often plot log-log plot or semi log plots rather than arithmetic plots. I found the reason now!! Connected all the points 🦋Excellent 🙌😍
Hi, Parth! Nice video. A nice continuation to it would be to highlight how log-scale linearization distorts the error distribution of the fitted parameters. Keep up the good work
Very nice trick and definitely useful for checking if there is a power law relationship in your data. However, a small problem with this approach is random errors in the measurements. When you take the logarithm of your measured B values, it can be thought that the logarithm actually operates on B + v where B is the 'true' values and v is a random measurement error. Then, when you do linear regression to estimate the parameters theta and r, the random error may cause your estimated parameters to be biased to some direction. To avoid the bias you could use nonlinear regression to estimate these parameters directly without taking the logarithm, but this makes the math a bit more difficult.
You mean, just use a computer to do the fit?
This is great! I wasn't aware of this. Thank you
One minor nitpicking point. While linear regression in the "log" space is a great start, I think you eventually want to do regression (non-linear) in the original space. doing regression in the log space is min (log(y) - (log(beta) + alpha*log(x)))^2 = min (log(y/(beta*x^alpha)))^2, which, as desired, has its minimum when the prediction and the target are equal, but under predictions are weighted more than over predictions, due to the asymmetry of log. For the best fit, I think you eventually want to solve for alpha and beta in the original space "min (y - beta*x^alpha)^2". I could be wrong on this.
A neat trick, this! The close relationship of logarithms to information comes to mind, which may show up here as how much storage -- how much complexity -- is required to massage the raw data into a log-log linear form. That's interesting by itself, but it gets "a bit" more interesting if one considers that it is the *lack* of information that most sharply defines the transition from classical-causal to quantum-indefinite physics.
Very nice explanation. During my experiment, I always used linear fitting to find some properties of a our fabricated diode.
Let there be light! Thanks! Used a long hand version of this to arrive at the relationship when those constants and power terms don't match a predicted value! Need to take maths seriously for all these easy tricks to make that task easier.
After reviewing this trick found those plot points are orbiting (helix) around that central point.
sir u literally are the best teacher there is on google more people should view ur channel its amazing thanku sir pls keep making more
First, the common logarithm (base 10) is usually used for log/log plots and log/log graphing paper is ruled in base 10 decades. Second, physicists use chi squared fits rather than linear regression such that data points that are well-known are weighted more heavily. Third, statistical and experimental fluctuations limit the knowledge gained by fitting data to a parametrized model. The graph shown is unlikely to have better than 1-2% tolerances in slope and intercept.
I’ve been recently learning about logarithms, and this is one of the coolest uses for them I’ve seen so far.
This video is so wonderful and amazing that it really created a huge explosion of intuitiveness in my brain!!
Keep it up parth sir!
Computer science people know this trick pretty universally when they're crunching data. Following chats on projects that are a little over my head, I hear "the graph is log/log, right?" or some variation all the time. Nice to see the y=mx+b(in the US) relationship: now it makes total sense.
I hope you know you're a hero to young physicists who yearn to explore their independent minds to think intuitively and diligently. You are the reason why my love for science has amplified. I'm contented that I found you're channel on youtube for inspiration. I hope I become a great physicist, and when I do, I'll make sure to credit your name for all the help you have given me. Thank You, friend.
Totally useful and fun! Thanks!
This is something you learn to do in any good collegiate introduction to statistics course. This was done in my AP Stats course, where we were given a graph that was obviously not linear but plotting it using the logarithm (base 10, which should change nothing) of the two variables makes our plots linear. This better helps us find the log(x_hat) and therefore our x_hat. It was a very nice trick and one I never realized was used so often.
I love this channel, I have watched the video about Lagrangian Mechanics and this one. You have an amazing way to explain and simplify stuff. Looking forward to new videos.
Clever i have to say.thats why i used to love physics in high school. Physics is nothing but using clever tricks to derive expressions for physical phenomenons. I love playing with equations . I remeber understanding calculas by using infinitesimally small change as the trick to integrate for irregular quantities like rotational inertia of a npn uniform body.
'Straight lines are more friendly. That's what it is' yes!!!
The shortest path between two points is a straight line. Gets rounded trajectory. Applies ln to it to speed it up.
Excellent video. Very interesting, informative and worthwhile video.
You’ve done it again. Brilliant video. Thanks
Your videos are incredibly simple and highly Intuitive, Thanks for sharing this knowledge
It would be nice to show also to people how to deal with interval of uncertainty of measurement after logarithmic transformation. How it modifies Gaussian curve. And overall how to count final interval for constants.
At least with pure wave functions (sines and cosines) you can take a complex log and beget the proportionality constant and power. In this case the power is analogous to the frequency and the proportionality is analogous to the amplitude. Phase shift would be a shift like f(x+a) analogous to a different start date. Then a linearization of these waves would be an absolute value function that oscillates between 2 y values a distance of 2A away from each other. This also leads to more exotic averages. The geometric mean is an exponentiation of the arithmetic mean so graphing it on a logarithmic scale would look easily similar to the arithmetic mean.
Excellent presentation, clear and concise. The way it was presented to me as I started my research: "The power law is very forgiving." It gets a bit hairy when you're trying to show the power law exponent is different to unity.
Wow this video was actually super enlightening. Nice going!
we always use this in electrical engineering and electronics engineering. but most frequent this is used in variable frequency applications.
Consider , "we are conducting"...
I thought electrically..😂😂...
But we are conducting an experiment.
I've really really been frustrated because of why the hell we use log and lan xD Thanks to ya for making this our parth!
Brilliant trick. I agree that plotting straight lines is superior as they easily compare with other straight lines. In telecom, we go as far as to use a double Log axis when plotting bit error rate vs power (in dBm).
OMG. This is the most power video I have ever seen. SO simple and yet VERY VERY POWERFUL 🥸
Brilliant! This was a simple, yet powerful explanation of why logs are so cool. Nice job.
this is just the basic stuffs its taught to 8th std kids in India
@@siddharth5339
Ok no one cares, people only care about application.
@@studiousboy644 ya we do buddy we know the application i dont speak for all but for myself yes ik what it is
@@siddharth5339 *me and the bois looking for who asked*
@@siddharth5339 Not really! Although this is a basic mathematical concept, what you said isn't true. Indian schools mostly make the students rote-learn all the formulae and short-cuts to find the answer by substitution. Or else, they make the students rote-learn high level definitions and understanding of concepts. Ask any Indian high school or even a college kid some questions related to application or basic implementation of these concepts and we'll completely draw a blank. We can also see this in all of those TH-cam videos where Indians are explaining science or engineering concepts - they're just repeating exactly what you'll find in a text book already.
So crazy - thought I was up and running with things for years, looks like there are always new tricks to put them in my bag of tricks... so obvious about taking log only after watching this tricky-maths video.
One more thing to add: The exponent is by definition dimensionless, and since the equations of physically measured variables require units to be consistent on each side, it is extremely unlikely for the exponent to be anything other than an integer or half integer. After all, the a distance measured in meters raised to the 2.0249th power means the coefficient has some *awfully* heavy lifting to do in order to help such a strange denomination of meters conspire to equate to Newtons on the other side (or whatever the units work out in a given relationship).
This fact lets you round the exponents and see the deviation as something hidden in your experimental setup or measurement techniques.
Nice video! I just want to add that even polynomial laws don't have straight line log-log plots, even lines! So if you have a law where y = ax + b for example, the log-log plot will be curved. For lines and parabolas, you can use translations to straighten out the plot, but there's nothing that can be done for cubic polynomials and above. I think a lot of people confuse power laws and polynomials laws, since the former is a subset of the latter, but in this case it's an important distinction to be made.
I would use gradient of the line in direction of perpendicular line. We can find three different reasons for that. One reason is that it is geometrically dual vector (also Hodge dual to movement vectors on line) and line elements are created by points on tangent space starting at some point of the line. The Hodge dual in 2D to any vector in direction of the line is again a vector and it coincides with normal vector of the line. And normal vector of the line is its gradient.
The reasons for that:
1) inner product or duality
2) analytical geometry, how equation of the line is constructed in a point way (dual construction to its vector way)
3) differential geometry - gradient is perpendicular to contour line at given point
4) symmetry - gradient splits equally the curve at some point
Also consider gradient appearing in the principle of virtual work.
Not only for powers, it works for exponentials too! I actually used it in a protocol just a few weeks ago
in some what related manner, I feel like this how deep neural network works, essentially try to take real life highly non-linear data, and gradually reduce the dimensionality and try to more "linear-ize" in each layer, until you get to the final layer which output an approximate linear function that correlate real life data to some derived parameters.
Cool! I would have tried polynomial fitting with l1-regularization to get the right exponent. But this is much more elegant.
This Man is my inspiration.
Learned this in my physical chemistry lab for the first time this semester and I thought it was absolutely brilliant
LMAO great title. Great content, too! Always happy to find a smaller(-ish) science channel. Subbed!
This is really cool and simpler then I would have thought!
I hope everybody know that linear fit on log-log is not the optimal regression (minimizing sum of failure squares)
Hey Parth great content, i would love to see more videos related to Experimental Physics please keep doing this. thank you for such great videos
I used to tell my students that everything we plot in Physics is going to give us a line, even if we think it should be a curve. They looked at me like I just landed in a spaceship from Mars because we had just looked at several common relationships (y =kx, y =kx^2, y = k/x, etc.) and the curves they generate.
6:24 for some strange reason in the United States we use b instead of c for the y-intercept. using c makes more sense to me, but we are stuck with b.
Such a clear explanation! Thanks!
Excellent explanation and very nice visuals. I almost didn't watch this though, because I was put off by the title! There is so much click bait on TH-cam that uses these over-the-top, all-caps HATES! phrases, that I wonder if you shouldn't perhaps consider using something more in keeping with your content? Again, the content is wonderful, just a comment on the title.
Great tip thanks!
The only thing I would mention is that the diode plot is only curved for very low voltages. After that (beyond the bias voltage) it’s nice and straight.
it's not in fact. it's an exponential.
I knew about this already, think I saw it for the first time from 3Blue1Brown in the fractal dimensions video probably. I love the elegance of it.
Good Info..I had tried plotting a curve by curve fitting...and did some guesswork to find constant and power. but this plotting log-log graph is good. Now I understand importance of semilog paper
Can you please talk about the Bohm/De Broglie interpretation in a future vid? It would be awesome!!
My goodness I used this all the time in my physics lab in +1 & +2 but never thought about why are logarithms being used here!! Thank you so much Parth this was amazing 🤩🤩
My mind is blown, Parth!
Reminds me that I have learnt more from TH-cam than from books.
Fantastic tutorial. Love this channel.
Bro you are my inspiration just continue what you are doing...♥️
Wow, consider myself reasonably mathematically competent but didn’t know this. Makes perfect sense, thank you!
We used this for the ezperiments in the physics lab in Chile, really cool trick
Awesome!
Thank you for an excellent and concise explanation that was easy to understand. Bravo, Parth!
F=gm1m2/r*2. I’m learning about that now
Another excellent video from Parth. Thanks for the clear explanations!
we need more experimental physics
Parth is a very good teacher !
The only problem is that you have to be careful about the propagation of incertitude (error bars) ! :) So this method will not produce good results if you don't have error associated to your data. Also non-linear regression are not so hard to do with good programs like ROOT
This is a very slick method.
Wonderfully Explained..
In Indian Carnatic music.. there's a way word for "Explaining or Expressing things in simpler way"..
The word, " KAKAPADAM" mean...
" As easy as peeling out banana."..
This Suits Parth's Way of Physics 😊
Thats true!!!
That's very kind, thanks! I should learn more Carnatic music :)
Thank you for the linear explanation. 📏
ok, this was experimental physics 101. you have to do this kind of stuff pretty early even in engineering
This kind of stuff is done a lot in undergrad/grad physics.
exceptionally well explained
As a former professional biotechnical analist I completely relate to this and want to add: by using a linear progression analysis you can give real estimates of the confidence of your data if you have enough measurements.
That's what made slide rules so powerful before calculators became available.
Awesome!!
Thank you for providing this wonderful and useful explanation of logarithms.
But, speaking of physics, most of the quantities have unit.
Is it okay to directly put logarithms on those quantities?
Let's say, the length of a rope is 1 m which equals to 100 cm;
however Log(1 m) doesn't equal to Log(100 cm).
I really get confused, cuz I've seen lot of quantities that are under logarithms symbol by many physicists.
That's a really interesting question!! Apparently from what I found, the logarithm can only be taken of a dimensionless (no unit) quantity, and thus when applying it to a quantity with units one is actually finding the logarithm of the quantity as if it were dimensionless. So something like log(18 s) cannot be treated rigorously but is instead moreso a shorthand for log(18 s / 1 s) = log(18).
I believe that the reason this still can be applied to relationships between physical quantities is because such relationships hold true regardless of units: for example, F=ma is not an equation with units, but instead one that requires all of the units to "agree" with each other for it to provide any meaningful information.
Main reference for the first part is math.stackexchange.com/questions/238390/units-of-a-log-of-a-physical-quantity, they link a very interesting journal article that's worth a read.
There are real problems with using this routine rather than employing a good, weighted, nonlinear regression routine. One obvious problem is that routines employing ln(data) improperly suppress the larger standard deviations. Another problem is that one often should use the result when the independent variable is 0, which cannot be done with ln(data).
I never knew this. If I did, I have long forgotten it. Thank you.
I am wondering why most teachers (or at least the ones I know) most of the time make things much harder than they really are. Than you @Parth G for your videos.
our teacher taught us that method to establish relations between different values
amazing work :3/ thanks for explaining it to us. love you ,
Great video! I finally found out why logarithms are so useful.