12:36 This is for my own reference. Hands down the best and most complete video on logarithms I've ever seen on RU-vid. History and use included. I like it.
I think the story-telling approach of explaining something complex like the natural log is very powerful and it should be done more regularly in schools. Well-done!
Thanks. I find that I don't fully understand a concept until I learn about its history, motivations, etc. and I agree regarding using this approach in schools
@@tareksaid81 Yep. The Physics text book I had in high school in the early '70's took this approach and for me it worked well. Learning is about connecting information chunks.
@@tareksaid81I think it had to do with the nature of school creation. Schools were created to produce employable engineers en masse, who are able to understand basic maths like sum, products, exponents and logarithms and who obey to what they are being told(so less incentive to promote thinkers). I think that's the reason, but it's my theory though.
@@ze_kangz932 I have a similar theory. That's why one of my favourite quotes, which is attributed to Mark Twain: "I have never let schooling interfere with my education"
Bravo! One of the most enjoyable videos I’ve watched on RU-vid. I think math would be easier to understand if first taught from the historical perspective of man progressing to president day.
I am really glad you enjoyed the video Matthew. I totally agree regarding understanding maths through history. Mathematical ideas usually start simple and intuitive, but over the years they get more and more abstract. While they are more powerful in the abstract form, they are also more difficult to understand
It's likely beyond the communication powers (har har) between teacher and schoolchildren But it DOES make far more sense, when you realise WHY the genius mathematicians were creating these math engines Maths is mostly taught parrot fashion and we're all taught multiplication (and logarithmic) tables and then given exercises to complete (or else!) It should be de riguer for all math lessons to make the boilerplate statement that logarithms were just quicker to calculate before electronic calculating machines were invented! Addendum: I remember reading about the human calculator service before WW2 When scientists at Los Alamos and universities had too much maths and too little time, they'd actually phone or snail mail a bunch of guys who would do the MENTAT heavy lifting for them!!
@@tareksaid81 , it may have been called Natural Logarithm due to its derivation from an area under a hyperbole. Unlike other logarithms that can be artificially set such as the Common Logarithm of base ten or any arbitrary base.
You really deserve a bigger audience. What is fascinating in mathematics is the line of reasoning that mathematicians follow to arrive at a concept. More so when the reasoning is rooted in experience and application. This is true intellectual discovery, and unfortunately far too often omitted form math class. Thank you for this video, I enjoyed it a lot and immediately subscribed your channel. Looking forward to more videos from you!
Thanks, I am working on it. I totally agree and I think maths would be much easier to understand if it was taught from a historic perspective. The thing with maths though is that over time, concepts become more rigorous but at the same time they become more abstract. Maths education today focuses on teaching those abstract concepts as they are more rigorous. Thanks for the sub, I hope you will like future videos too
Fantastic! It is amazing that I can now create logarithms of my own at home, accurately, instead of googling everything. Thank you for this history. Few, very few people could have explained what you just did. Genius mind, sir.
Thanks for your kind words Geo. I really appreciate it and it means a lot. I am glad you liked the video. My next video is going to be about the history of calculus. Hope you like that one too
I never comment under a video, because I believe my commemt can't add much to the conversation; but this time I must let you know: this is the best maths related video I've ever seen (and I've seen a lot!). You beautifully conveied the idea of what mathematics was like in its early stages, before widespread standardisation, when being a mathematician wasn't associated with rigor and stiffness, but rather mathematics was creative, imaginative and required a deep personal understanding of numbers (and it probably was even more different than I can imagine). This really gives an idea of how knoledge transforms through history and how we are boxed into the way of thinking predominant during our life. Many thanks for this piece of art! P.s. saved the video so I can watch it again when I'll have forgotten how great it is
Such a wonderful and touching comment. I really deeply appreciate it. I took a snapshot of it and shared it with family and friends :) Indeed, I like to think of mathematics as a creative, artistic pursuit. While I believe that rigour is important, there still should be place for intuition, both in teaching and in discovering new ideas. Over the last year, I've been researching the history of calculus, it is amazing how playful and risk taking (almost reckless) the pioneers were, particularly with the use of infinitesimals. Thank you, I feel more motivated to keep doing what I am doing!
This is so beautiful. 10:37 was such an aha moment. Can't stop smiling and thinking about it. Watched the video like 2 hrs ago. Had to come back and leave this comment
Very well-written and demonstrated historical dive! An aside about the time between Napier and Euler: as I understand it, e as a number alone was first described by Bernoulli around 1685 as a compound interest problem, whose solution he gave as a series and estimated to be between 2.5 and 3. Not as precise as Euler's estimation, but it's interesting how many stages there were getting to the constant we know now.
Jude, this is a very touching comment and I deeply appreciate it. When I was working on the video I wanted to share the sense of beauty I felt when I first learned about these concepts, not just the information. I am glad it came through. Thanks for sharing
Really interesting, the way people int the past thought about logarithms is so different from what we know now. I'm glad someone thought to cover this topic! However, I think you could have expanded a bit more on how people got from the hyperbolic logarithm to understanding that it has links to exponentials.
Thanks Daniel, I really appreciate your feedback. The original plan was to talk about how the connection of logarithms with exponentials was discovered but then I realised that it would probably be another 20 minutes and thought that the video might get too long. Perhaps I will do a future video about it.
Nowadays we take for granted a lot of things and forget the work of many to get us here. Fascinating video showing the work of these great mathematicians!
It’s my pleasure Pashkuli, I am glad you liked it. I do believe using history to teach mathematics would help many students have a better grip on the subject
@@tareksaid81 Yes, I think you are right! Today math is taught as a result or most applicable method. The thing is in History there have been so many things in math\physics that teaching their origins and historical sources would take years only for a few subjects\problems. Your video is great in that regard! You have to do more of these!
@@PASHKULI Exactly. Teaching the history of the subject takes a lot longer than teaching the final results and the education system can not afford that. That's why we have RU-vid :) Working on the history of calculus at the moment. Hope you will like it
wow.. thanks for your kind words and encouragement. I had a similar feeling when I first learned about that connection. I am really glad it has been conveyed in the video :)
Thanks Yohan, I am glad this video helped in making the concept clear. I really believe that when we look at history of any concept a lot of things become much clearer.
This is one of the best videos ever on this topic - hell, it IS the best. As a High school student it feels illegal to know all this and to have gotten it for free. Thank you so much.
Ha ha. Your comment made me laugh out loud :D Thanks for your kind words and support, I’m really glad you liked it. I remember when I was in high school I was frustrated with the concept of the natural logarithm but I didn’t have the resources to research it. I’m glad the world has changed a lot since then and now we can get this information for free :)
Thank you for this very clear explanation of how the natural logarithm appeared. I knew a bit of this history, but learned of lot more viewing your explanations.
Wow, that was most fascinating math video I have ever seen . The derivation for area under the curve you used without integration is really mind blowing. You earned yourself one new subscriber.
Thank you. I worked with a genius many years ago. His application of Logarithmic principles with sales data was epic. Lotus123 (Ln) and SPSS (Floppy disc)! Mercator, King of maps too. Fantastic explanation.
That sounds interesting. I am intrigued about how he did it! Btw, this is a different Mercator to the one who studied maps, the cartographer is Gerardus Mercator, while the mathematician os Nicholas Mercator
@@tareksaid81Thank you for the clarification re. Mercator the mathematician and the Cartographer! Converting standard sales metrics to LN scale to better quantify growth/decline and to aid accurate forecasts is what I remember. Then the pencil, pad and scientific calculator came out and I was lost!
Beautifully explained!!!! It's so wonderful when math is put into the context of history and see how time shaped the evolution of various concepts. Math should always be learnt with its history. This is an absolute must for any school student beginning his journey in logarithms
Thanks for your kind words Leo. It means a lot. I agree, I find that learning mathematics and science through history makes things a lot clearer and less mysterious
We are Very Thankful To you for These VDO In Which Discovery of Natural Logarithms Properly Explain ed Effort Of Sir John Napeir ; Euler n Other Mathematician is Remarkable We are Thankful to All of Them
I have a calculus book that assumed logarithms as well as trig functions are calculated using tables. It was a wild concept. But also made a lot of sense, it was a very cool piece of history which is now lost
Interesting. I found out that logarithms were still in use up till the 70s and probably the 80s. They were the main "calculator" for over 350 years! It is very cool indeed
@@tareksaid81 Yup, it was "Calculus Made Easy" which apparently was first written in 1910 (Far older than what I thought). And it has a heavy emphasis on log-tables exponential-tables and sine-tables for the chapters related to those concepts
Logarithms was a mystery to me. Although i used it quite mechanically. I thought that it was to make hyperbole curve a linear one. But it’s much more than just that.
I agree, in general I think teaching mathematics through its history is probably more beneficial than teaching it abstractly. Thanks for your kind words, I really appreciate it :)
Fantastic story to be replicated in math classes. Thanks for the effort to present your story of the logarithm. The name "logarithm" probably originates from the word LOGOS (Order or law) and RITHM (Harmony), resulting in something like ORDERLY HARMONY!
This is the way it should be taught in school so that the logic of how it relates is understood without just telling students to learn by rote and memory alone.
Fabulous.....It's really amazing how you broke down Logarithms into small easily-digestible chunks......looking forward to the long road of understanding QM....keep up the great work.......
Thanks Sherif, I’m glad you liked the break down of logarithms and I really appreciate your comment. I’m currently working on QM in parallel with working on the calculus series. My aim is to break it down to small steps as well. Currently studying Heisenberg’s paper that started it all. Really fascinating stuff that I haven’t seen in any textbooks or videos. I hope I’ll do it justice and that you’d like it :)
This was only one of the streams where the significance of the constant e was discovered near the same time.. In 1683 Jacob Bernoulli was following a question about compounding interest where he noticed that compounding more and more often approaches a limit of e as the time interval approaches zero. Specifically, he showed (1+1÷n)^n approaches e as n approaches infinity.
That's correct Christopher. This video however is more about the natural logarithm than it is about the number e. Also, while Bernoulli identified the formula for the number e, he wasn't able to calculate it, neither did he relate it to logarithms. Things came together eventually with Euler
Thanks I really appreciate it. I agree - The original plan was to talk about how Newton/Mercator came up with the series, how the relation between logarithms and exponentials was discovered and how Euler calculated the base of the natural logarithm. But then I realised it would be a very long video and I had to draw the line somewhere :)
Thanks Ravi. I’m glad you found it helpful. Currently working on the history of calculus and I uploaded the first video already. Hope you’ll like the series :)
I agree. I think it is because logarithms definition has changed over time from calculation tables to inverse function of exponentials and maths education focuses on teaching the latest concepts. I do believe though that having a historic perspective is very important as it makes the topic more accessible and at the same time makes us appreciate the abstract concepts more.
Thanks Faisal, its funny how quickly log tables disappeared from schools once calculators were introduced. I went to high school in the 90s and didn't study anything about log tables back then!
e is so basic to things people have been interested in for thousands of years, like interest payments. Its weird that there are not records of its earlier use. People have been really good at the maths needed for various forms of accounting since the earliest literate civilisations we know of.
I think one reason that there are no earlier records of e was the difficulty in calculating it. For example even Jacob Bernoulli, who was the first to recognise the existence of e, was only able to calculate its value to between 2.5 and 3
nice explanation, I was using log for easy calculation and converting multiply to adding, and the power to multiplication, and was preparing a demo for explaining that, and I see this video did it nicely, but you can add to this video, to convert powers to multiplications
I am a Criminal Lawyer.. if you could explain math to me then you must great! What a wonderful explanation. Please let me know how I can support the awesome work you are doing. I am now watching all your videos and taking down notes - the subject has never been so fascinating!
Thanks a lot for the lovely comment Tapan. I really appreciate it. The whole reason I started doing videos is to share the beauty of mathematics with the world and not just with the math minded as I really believe it is a form of art that needs to be shared. Comments like yours really makes me happy. You can support the videos by liking and sharing or by supporting me on “buy me a coffee”. at the following link: www.buymeacoffee.com/tareksaid Thanks again, your comment made my day :)
WOW...Teaching is really a gift. Electrical Engineer for 20 years I finally get the right meaning of logs. You should write a book called "How to teach mathematics" or "The art of Maths teaching"...ha ha ha
Thanks, I am really glad you found it easy to understand and I am doing now a series on the history of calculus. Will be releasing part 3 asap. I hope you'll like it
There is an old joke that after the Flood, when Noah commanded the animals to go forth and multiply, the pair of adders came up to him and said, 'Sir, we cannot multiply, we're adders.' So he made them a log table and they multiplied under that.
With all these professional mathematicians saying "Wow, I never knew this", I can only ask: why the heck isn't this teaching approach used in math classes? I never understood the natural log/e either. Now I do. People talk about how AI will change education. Forget that. RU-vid and the Khan Academy have changed education forever. Someone, somewhere, has made the perfect video explaining concept "X". Find the video, show it to your class, and discuss. (And if they haven't yet, any REAL educator with REAL expertise in "X" ought to be able to make the video themselves, even if they need help with the filming and editing and scriptwriting parts.)
I'm glad the video helped you in understanding the natural logarithm Tarl. Regarding your question about why this approach isn't commonly used in schools, it's likely due to concerns about mathematical rigour. Explaining the natural log in terms of the relationship between arithmetic and geometric progressions with small bases implies the use of infinitesimals. While it is a more intuitive approach, it is not considered rigorous (at least not in non-standard analysis framework) The education system has generally placed a higher value on rigorous proofs and formalisms than on intuition and conceptual understanding. However, I personally believe that developing intuition is essential for truly understanding mathematical concepts, and that rigorous proofs should be introduced once a strong foundation of intuition has been built. I agree, RU-vid changed education forever and I believe we will keep seeing different approaches to explaining the same concept which gives us a deeper understanding of a topic overall
Long story short: Back then maths was mostly number theory and geometry. So every new idea was filtered through one of these viewpoints. Way before the analytical approach, people were interested in the area under the hyperbola, i.e., the curve defined by y=1/x. The area under this curve after restricting the domain to the interval [1,a] is log(a). Back then, they defined log(a) this way. Nowadays, we define e and the natural logarithm, and after proving the Newton-Leibniz formula, it is clear that int_{1}^{a} 1/x = log(a)-log(1)=log(a).
Excellent summary and explanation of the change of the viewpoints in mathematics and how this applies to the change of the definition of logarithms. I am currently working on a series about the history of calculus and for the time being I am adopting the geometric and infinitesimal viewpoints in explaining the basics before moving towards more abstract definitions. I find this approach more accessible
@@tareksaid81 I would definitely watch that. I agree that such an introduction can be helpful to create a strong basis of intuition. However, overdoing it could be counterproductive. It was actually slowing down the progress of differential and integral calculus that all results and all proofs had to be somehow explained via geometrical concepts. See Newton's original proof about the gravitational force field induced by a homogeneous shell (being zero inside the hollow space, and being identical to that induced by a mass point outside the shell). It is somewhat awkward and roundabout. Abstraction and the language of multivariate calculus is helpful there.
@@andraspongracz5996 I totally agree. And in fact it is probably the reason that curricula today don't use infinitesimals anymore, as now we have a rigorous formulation of calculus and using infinitesimals seems like taking a step backwards! I will make sure that after I establish some intuition around calculus I will move into more rigorous explanation. Thanks for your insights, I may ask you questions in the future if that's ok?
