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Tarek Said
Australia
Registrace 27. 02. 2022
My aim is to make complex ideas simple through telling their stories.
The channel idea came to me when I was reading about the history of quantum mechanics and found out how Werner Heisenberg came up with matrix mechanics before he even knew anything about matrices! This gave me an understanding of QM that no textbook could give me and I thought it would be interesting to share this knowledge on CZcams. I started working on the history of QM but then I realised that it was massive and that I should start smaller and work my way towards it. So upcoming videos will be supporting the main project of the history of QM and they include but not limited to:
The story of calculus
The story of differential equations
The story of Fourier transform
The story of linear algebra
The story of Maxwell equations
The story of quantum mechanics
The channel idea came to me when I was reading about the history of quantum mechanics and found out how Werner Heisenberg came up with matrix mechanics before he even knew anything about matrices! This gave me an understanding of QM that no textbook could give me and I thought it would be interesting to share this knowledge on CZcams. I started working on the history of QM but then I realised that it was massive and that I should start smaller and work my way towards it. So upcoming videos will be supporting the main project of the history of QM and they include but not limited to:
The story of calculus
The story of differential equations
The story of Fourier transform
The story of linear algebra
The story of Maxwell equations
The story of quantum mechanics
History of Calculus: Part 3 - The Historical Motivation
This is part 3 of the series: History of Calculus. Where I talk about the origins of calculus from ancient times to modern history.
In this video I talk about the motivations that led to the discovery of calculus.
To support this channel:
- Buy me a coffee: www.buymeacoffee.com/tareksaid
- Patreon: www.patreon.com/tareksaid
- Super Thanks: You can find it by clicking the 3 dots under the video
Notes:
- 0:05 The work of the ancient Greek mathematicians was forgotten and was confined to libraries scattered around the mediterranean. Almost a thousand years later, Arab and Muslim scholars translated the works of the ancient Greeks and revived some interest in studying curves, and although they made great contributions to the study of curves, they stayed within the limits of the method of exhaustion.
- 0:05 During the 2000 years' gap, mathematicians in India, particularly in Kerala school of Astronomy and Mathematics, made discoveries similar to what we may call today calculus, while their work is brilliant and has elements of calculus, it can not be called calculus. I will make a separate video about their brilliant work in a later video in the series as it gives an understanding of calculus from a different perspective. One based on arithmetic more than on curves.
- 1:13 It is important to note that many mathematicians are not necessarily motivated by the practical applications of mathematics and are interested in mathematics as a form of art, however, when other factors like political, cultural and economical are at play, we can see how the absence of the practical applications of geometry shifted the focus away from it.
- 7:25 Galileo later found that the motion of objects in free fall is uniformly uniform.
- 13:34 Such a rod doesn't exist in nature and is used for demonstration purposes only.
- 15:07 Finding the differential equation of the water from a tap is not possible since it is assumed to be done randomly.
-17:06 The origin of the cycloid is not clear, some historians proposed that it was known to the ancients, while others think it was discovered in the 15th century and others proposed that it was only discovered in the 17th century.
- 20:29 The Copernican model was already known at the time but it wasn't accepted. Another model that also existed was proposed by Tycho Brahe. Tycho assumed that the planets revolved around the sun, but the sun revolved around the Earth. Having said that, the most commonly accepted system at the time was the Ptolemaic system which is the one shown in the video.
References:
- The Historical Development of the Calculus | C.H. Edwards
- The Origins of Infinitesimal Calculus | Margaret E. Baron
- The History of the Calculus and its Conceptual Development | Carl B. Boyer
- Infinite Powers | Steven H. Strogatz
- Calculus Reordered | David M. Bressoud
- Historical Stages in the Definition of Curves | Carl B. Boyer
In this video I talk about the motivations that led to the discovery of calculus.
To support this channel:
- Buy me a coffee: www.buymeacoffee.com/tareksaid
- Patreon: www.patreon.com/tareksaid
- Super Thanks: You can find it by clicking the 3 dots under the video
Notes:
- 0:05 The work of the ancient Greek mathematicians was forgotten and was confined to libraries scattered around the mediterranean. Almost a thousand years later, Arab and Muslim scholars translated the works of the ancient Greeks and revived some interest in studying curves, and although they made great contributions to the study of curves, they stayed within the limits of the method of exhaustion.
- 0:05 During the 2000 years' gap, mathematicians in India, particularly in Kerala school of Astronomy and Mathematics, made discoveries similar to what we may call today calculus, while their work is brilliant and has elements of calculus, it can not be called calculus. I will make a separate video about their brilliant work in a later video in the series as it gives an understanding of calculus from a different perspective. One based on arithmetic more than on curves.
- 1:13 It is important to note that many mathematicians are not necessarily motivated by the practical applications of mathematics and are interested in mathematics as a form of art, however, when other factors like political, cultural and economical are at play, we can see how the absence of the practical applications of geometry shifted the focus away from it.
- 7:25 Galileo later found that the motion of objects in free fall is uniformly uniform.
- 13:34 Such a rod doesn't exist in nature and is used for demonstration purposes only.
- 15:07 Finding the differential equation of the water from a tap is not possible since it is assumed to be done randomly.
-17:06 The origin of the cycloid is not clear, some historians proposed that it was known to the ancients, while others think it was discovered in the 15th century and others proposed that it was only discovered in the 17th century.
- 20:29 The Copernican model was already known at the time but it wasn't accepted. Another model that also existed was proposed by Tycho Brahe. Tycho assumed that the planets revolved around the sun, but the sun revolved around the Earth. Having said that, the most commonly accepted system at the time was the Ptolemaic system which is the one shown in the video.
References:
- The Historical Development of the Calculus | C.H. Edwards
- The Origins of Infinitesimal Calculus | Margaret E. Baron
- The History of the Calculus and its Conceptual Development | Carl B. Boyer
- Infinite Powers | Steven H. Strogatz
- Calculus Reordered | David M. Bressoud
- Historical Stages in the Definition of Curves | Carl B. Boyer
zhlédnutí: 12 954
Video
History of Calculus: Part 2 - Calculus in the Ancient World
zhlédnutí 16KPřed rokem
This is part 2 of the series: History of Calculus. Where I talk about the origins of calculus from ancient times to modern history. In this video I talk about the first two of the five methods that calculus evolved from: The method of dissection in ancient Egypt and the method of exhaustion in ancient Greece. I believe that the best way to understand a complex topic is to go through its history...
History of Calculus: Part 1 - Calculus in a Nutshell
zhlédnutí 27KPřed rokem
This is the first part of a series about the history of calculus. I wanted with this video to build a general overview of calculus by answering three main questions: 1. (0:26) What is calculus? 2. (2:50) Why do we need it? 3. (4:03) How does it work? I tried to stay in this video on a very high level without digging much into mathematics as we are just starting :) I hope you find it helpful and...
The History of the Natural Logarithm - How was it discovered?
zhlédnutí 504KPřed 2 lety
- Learning about the history of the natural logarithm helps us understand what it is. Today we define the natural logarithm as a logarithm with the base e and many people, understandably, wonder why! Interestingly the natural logarithm was discovered decades before the number e. In fact it was discovered before the link between logarithms and exponentials was recognized! In this video I talk ab...
the history behind a concept- if only all teachers explained them as good as Tarek does...!
Finally we have a man who can explain what logarithm is in a layman way. Thanks.
Your videos are very nice and informative , please upload more videos❤
Thank you, I am an engineer, and we were never explained Integration, Derivatives and Logarithms the way you explained. I am sure it is not explained now too. We were just mugging up and following steps, without understanding it. Exams were more important. Thank you so much Tarek.
You seem very knowledgeable about the history of mathematics. May I know your credentials? Or at least, what your interests are that align so good for these videos?
My background is in electrical engineering and I am very interested in reading history, particularly the history of mathematics and science as I believe it is the best way to deeply understand a topic. I am also a communication skills coach. I hope this helps :)
One thing is not explained in the video, namely: 8 x 32 = 256 and respectively 3 + 5 = 8, and everything is correct, you can easily check the multiplication result by comparing it with addition, but as mentioned, the table doesn't cover all the numbers. When Nepper wanted to solve this problem and multiplied the terms of the geometric progression (left side of the table created in 3 min and 38 sec movie) by 0.999999 and reversed the order of the terms, everything stopped matching, he started the left side of the table from 10000000, not from 1, and each next term was smaller than the previous one and the original words increased by a specific constant amount. Now geometric progression not matching to arithmetic progression and mathematical operations not matching too. How Nepper matched the right side of the table? Has he reversed right side of the table too?
Excellent observation. I do mention in the description of the video that "For Napier’s logarithms to work with multiplication and division, we have to divide by 10^7." I am not sure why Napier chose to start with 10,000,000 instead of 1 since the calculation involves dividing back with 10,000,000 anyway. My guess is to avoid writing decimal points all the time. Interestingly, Henry Briggs later met with Napier and suggested that they go the other way around and to choose log of 1 to be zero (instead of log 10,000,000 to be zero), log of 10 =1, log of 100 = 3 and so on. Napier said he was too old to do all the calculations again and suggested that Briggs does it instead. Briggs did exactly that and created what came to be known as the common logarithm (log base 10) which became the main type of logarithmic tables for over three centuries. Napier's logarithms were the origins of logarithms but they weren't very easy to use mainly because of the point you mentioned.
@@tareksaid81 Thank You for answer, I agree that Napier's logarithms weren't easy to use after all it was begenning logarithms and we have to memory that not only Napier was creating it, many mathmaticians throught history creating this part of mathamtic, so not everything worked right away perfect and some things needed tweaking ...
When fourth part 🥹🥹
I know it is been too long :( I am working on parts 4 and 5 and will publish them together as part 4 is going to be very short
Let me add my idea found recently to explain the cut and stitch method. Always cut shape into what you already know at least or approximately like square,rectangle ,yriangle,trapezium , parallelogram not iregular shapeand stitch back.
Thank you very much. Please keep creating this type of videos.
Thanks for the encouragement Gautam. I really appreciate it. I will be releasing the next two videos together. I hope you would like them. It is taking long as I am juggling between my business and this
Waaaaaaaah! When is the next video?!😫
I am working on it constantly. I will be releasing videos 4 and 5 of the series together. I hope you would like them
Wonderful a d brilliant. Thanks God that i stumbled upon your this video because since long, i was trying to know the background and story behind the Mathematical formula/tables which we use frequently. Thank you very much. May God bless you. I am from India.
I am really glad that you liked the video Gautam and that you found what you were looking for. My greetings to you and to India :)
really extremely good job
i have rewatched them all like 3 times man!!
Oh wow. I am really glad you liked them. Thanks for sharing :)
I thought Logos meant word or reason and analogous means proportional?
Yes indeed logos does mean reason, but apparently it also means proportional. While I am not a linguist, I think it is similar to the root word "ratio" in English. In English ratio means proportion. And rational means proportional. But rational also means logical. I think it might be the same with the word "logos" in Greek
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.
Yes,now the penny has dropped for why anything raised to the power (exponent of) 0 is itself.Because it has no or 0 progression therefore in logarithmic terms it is just added to itself! i.e 10 exponent 0 is 10.
Interesting. Do you mean though that anything raised to the power of 0 is 1 (not itself)? I haven't thought before of using geometric and arithmetic progressions to show how something to the power of 0 is equal to 1. But I think it is a very good way of explaining it
how did he multiply no million times?
I am not sure I understood the quesiton Anna!
@@tareksaid81 to make the log tables
Great
This is simply great wonderful TAREK !we were taught Log Tables 50/years back. -We were so bored that Used to Throw Paper Rockets on each other 😮Now of course bit late you explained How JOHN NAPIER arrived on LOGARITHM
Thanks, I am glad you liked the video. hahaha.. that's a cool memory. Were they rockets made out of log tables paper ;)
@@tareksaid81 RULED PAPER 😮! ! folded
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
This is a wonderful series. It is very illuminating, very enjoyable to watch, and with a great narrating style. Please continue until its logical conclusion. It is a gem!
Thanks a lot for your kind words and encouragement. I really appreciate it. I am determined to finish the series :) I know it has been taking me so long, but I am getting there. I am currently working on parts 4 and 5 and will release them together. I hope you'd like them
Thank you so much ❤
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!
Thanks Casisus, I am glad you liked it. I was mind blown when I learned that Napier spent 20 years in writing his logarithms book!
That was excellent, and fun. Thank you.
Thanks! Great series so far, looking forward to the future videos 👍🏽 👌🏽.
Thanks for your support Hendrick. It really means the world to me and I deeply appreciate it. I am currently working on parts 4 and 5 and will be releasing them together. I hope you'd like them. Thanks again :)
Excelente vídeo. Mostrei ao meu filho que está estudando logaritmos na escola.
Thanks.. I hope your son found it useful :)
Logarithm made simple
Well, obviously if 2²=4 that means 2^x=4 s solution is 2 So i can see why they discovered it.
👏👏👏👏
Superb!
Excellent explanations, thank you 👍
Wow! Excellent presentation here. He is teaching some mathematical history here while also giving good insight into exactly what logarithms are. Thanks so much.
Thanks Jacob, I am really glad you liked it!
Thank you so much! Why isn’t this background part of every course on logarithms?
Thanks Nick, I am really glad you liked it. I did ask myself the same question when I was researching the topic!
I have a question for you. Could you imagine studying the history of mathematics without knowing the mathematics about which you are studying? Oh ... by the way, this was an excellent video.
Hmmm... I am not sure really. I would say that it would be like reading poetry translated to a different language, we would still get the essence of it, but we won't fully comprehend its beauty and nuances
@@tareksaid81 The reason I asked is that the history of technology is not typically studied by engineers or technologists. It's studied by historians with little or no technical training - just the ability to read what others have written. In several cases it's not the nuances they are missing. They've got it entirely wrong. Many thanks for your reply.
@@robertbarnett3980 Interesting. I didn't know that. I do believe that such topics are better studied by technical people. I do understand however how technical people might be more interested in the tech itself instead of its history
Seus vídeos são muito bem elaborados e agradáveis ao conhecimento. Espero que você conquiste, o mais rápido, milhões de inscritos ! ❤
Thanks for your wishes, I really appreciate it. I have to work on making more videos to get to a million :)
wonderful❤
Makes perfect sense. The only number you need to understand for the natural logarithm is 1, which is the slope. Everything else is trivial calculation.
Thanks.. I am not sure what you mean by that though 🤔
@@tareksaid81 Really? I'm surprised. e is the exponent for which the slope at 0 is 1, is it not?
waiting for next video
Coming soon. Will be releasing parts 4 and 5 together as part 4 will be a short transitional one
I salute you ❤❤❤❤❤👍👍👍🙏🙏🙏🙏
THanks Jitendra :)
Super interesting thank you
Thanks Simon
bravo!!!!
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
great video man!
Thanks Himani
Excellent
Excellent video, I was looking for something like this
Thanks... I am glad you found it :)
Holy shit, I dont remember when I have felt such an enlightenment and clarity after watching any math videos here. This series is so good, its like made from future, when they finally got how to teach properly. The design is also amazing. The author is definitely one of high souls living on planet our time. Thanks, and I wish you all the best!
What a lovely and encouraging comment. It really inspired me. I am currently working on parts 4 and 5 of the series and I must say I do have moments of doubt and I wonder about whether the effort is worth it. But then I read a comment like yours and it motivates me in those moments. Thanks a lot. I really appreciate it
Excelente explicação, com apoio gráfico de 1a linha. Surpreendente a precedência da descoberta do Logaritmo Natural antes do Número de Euler. 👏👏🎯
This was incredibly helpful. Instant subscription.