I forgot to mention the Fibonacci sequence! Leonardo of Pisa (Fibonacci) described the sequence F(0)=0, F(1)=1, F(n+1) = F(n) + F(n-1) in his book _Liber Abaci_ from 1202 in the context of a word problem about the breeding of rabbits. The sequence was known in Indian mathematics centuries earlier. The sequence does grow exponentially, but the formula F(n) = 1/Sqrt(5) (((1+Sqrt(5))/2)^n - ((1-Sqrt(5))/2)^n) was only written down in 1843 by Binet.
@@glowson3844 Just look for inscribed n-grams in a circle, understand the concept behind finding √x geometrically and you will understand why π and φ are directly related. Today we still use the linear approximation of π, which disregards the very small arc cuts, which contribute to the circum. and area. Hence π (the real, natural value) is just a tad larger. This is very important for astronomy and later will be for discovering dimensions.
@@fslurrehman True, but since the late medieval times (western) Europeans (brits, french, spanish, dutch) were the most "expansive" (means conquering) people, thus they took all the credits for "inventions". Iven the battery was invented in Mesopotamia\Iraq... but that is a different subject.
I loved this! Some more history of math should be taught in high school when introducing concepts, we take for granted a lot of impactful work that really had centuries of refinement and adjustement that now seems given by definition on a blackboard that has no relation to reality.
Exactly.. this way of methodology of teaching should be encouraged in physics, Chemistry, Literature, Biology as well as Mathematics. It gives spirit and enthusiasm to learn more about the subject. It will add value to what the teachers trying to convey teaching these formulas or subjects. I have always witnessed in the class asking some of our practical minded classmates “what all these knowledge will do good in my real life?” With the traditional teaching method we think that the knowledge we have been learning is to get high grades to be better than our classmates and to be excepted to better universities racing and succeeding in tests or exams in front of them. This kills the thirst for knowledge and thirst to try to do better than what is thought to us in school..
When there is a problem everybody needs to solve, people will find amazing solutions that look impossible at a first glance. I find that education system in most advanced countries are lacking on creativity, which I think it really impacts children to think of new ideas.
Yes people have always been smart enough to screw others with compound interests, and then smart enough to outlaw compound interests because they destroy common folks.
@@gelinrefira all interest is compound interest. It just describes how interest works over time. For example, you have 100$ in saving account with a 3% interest rate yearly. After one year you have 103 (3% of 100$ = 3 more dollars). After year 2 you don't have 106$, you have 106.09$ (3% of balance 103 = 3.09 more dollars). No one "invented compound interest". People came up with interest to get some money back on money they've loaned out. The math just describes how this accumulates over time. You are able to benefit from interest or compound interest just as much as anyone else. If you have a bank account you're benefitting from compound interest. If you have a single stock you're benefitting from compound interest (so long as you chose a good stock whose value goes up over time)
Since I last studied math for engineering about 45 years ago I had a very hard time keeping up with this video but I still find it fascinating that people were able and willing to produce such complicated work hundreds of years ago. I often wondered how and where all the log tables came from. I think I was one of the last engineering classes that used the slide rule for some of our classes.
Absolutely LOVE the history weaved throughout. Amazing, amazing video. Please do more - you have a gift for mathematical story telling. There are more and more people coming who speak the language of math - and this quality of video raises the bar. Reach out.
I’m sorry you had a shitty math teacher; math is humanity’s most beautiful / important creation, and it’s truly a tragedy that more people don’t appreciate it.
@@justinwatson1510 while I never did very well with other parts of the math curriculum, I did find an almost mystical fascination with geometry, so much so that I finished the whole years worth of geometry in six weeks. Occasionally I wish I had a similar experience with algebra. Maybe I will in my next life.
I had the exact opposite experience; I sucked at geometry in high school (I blame the shitty Georgia public school partly; the teacher was almost worse than useless) but algebra just made intuitive sense to me. I wasn’t able to appreciate geometry until after I got through differential equations or maybe linear algebra.
you act like its the teachers job to teach you that... they are there to see if you pass exams, stop being ungrateful. and people like you say stuff like "college should be free". education is not free stop whining
I don't get to learn about this part of math, the historical part, in school but it gives me so much more vigour and interest in mathematics. Thank you
Greetings from the U.K....Thank you for this... as a layperson interested in maths, all to often actually uses and examples are not talked about and even rarer the historical background to mathematical concepts... this helps immensely! Though I must say that even now, fifty years after leaving school I’m still waiting for that moment when a knowledge of trigonometry will save my life, as I was constantly told it would!
I believe math should be learned based on problems that need to be solved, rather than blindly memorizing formulas. So, to solve a specific problem, you'd try out many different methods with increasing sophistication, by first using the method used in the stone age, then with the method used in the year 1600, etc, until you arrive at the most efficient/advanced method, which also provides the correct answer. This way you acquire real knowledge and understanding of what you're doing.
But then, you would have to learn trig. before algebra. Good luck with that. I suppose it could be done. It would be interesting to learn how to solve things by numerical methods first now that computers are available to us.
@@ecavero1 That's true. Numerical methods are the way to go for basically all of math taught in schools and colleges. Its easier for us to think about and understand discrete rather than continuous sets. Who the hell knows what infinity means anyway -- e.g. limit goes to infinity? Give me a break. Math needs to be reformulated.
@@ecavero1 you need the math foundations to do it, im helping someone with a project on calculations for a rocket launch to orbit and ISS but everything is a struggle because they lack that foundation.
@@theremin_monkey limits are literally so usefull though. and you cant brute force simulate everything. even with supercomputers you cant (or it would benefit alot from a hybrid approach).
@ Daniel Rubin: what a fantastic 30 mins. I can appreciate the amt. of research and hard work that has gone into this. I have History of Science and math integrated into my STEM course for school students and 2 days are devoted to this entire subject (devoted to relationship between e and compound interest; the need for logarithms etc. ). this video has given me a refreshingly new perspective to make the class more enjoyable. Thanks a ton for this video
This is such an important video. I mean the historical context in which the maths was developed really helps one understand in which other contexts they are applicable.
@@DanielRubin1 no, thank you! It's because of this video that a^x=e^xlna isn't just another identity in a long anxiety inducing list of identities that I need to memorise and hope to recognise out of a pile of problems, but now I GET it. This has helped for topics in my applied maths AND pure maths courses
Interesting fact is at 11:25 the dice that you drew were illegal dice. A fact of standard dice is that opposite sides must add to 7. If you rotate one of the dice through what would presumably be the z axis, then you would have one side adding to 6 and the other adding to 8. This was not a criticism of your excellent video but an interesting piece of knowledge that I wanted to share.
I actually have a slide rule collection. 😅 I find them superior to electronic calculators in many ways, especially when the slide rule is specialized to perform a specific job. There are slide rules out there specifically designed to compute the frequency of resonant circuits, perform dead reckoning navigation, convert between Imperial and Metric...
Just want to say I understood nearly none of this (made it through Calc B but that’s it) but watched the whole thing because of how engaging of a speaker you are, and what a great history lesson too!
On the question of usury, it's a bit more complicated than that. Merely having Interest on loans was not condemned as usury by basically anybody; Rome had simple interest, and this wasn't completely outlawed even with the conversion of the Empire, or in the Byzantine period. The classical definition of usury for Catholics is charging interest either with what is known as an intrinisic title to interest, or charging interest in excess of any extrinsic title to interest. An intrinsic title would be built into the loan: I give you $1000, and insist you now owe me $2000, without any need for me to do any work or sustain any costs to deserve it. Extrinsic titles would be where you factor in stuff like the work I need to do to loan you the money, paperwork, paying for collection, and later on stuff like lost opportunity costs, inflation, lawyers to write up contracts, etc. The basic moral premise here is that the quid and the quo in a quid pro quo need to be equal, but in different modes; I pay you, the loaner, in accordance with the value of the service you provide, factoring in the work you did, and the costs you sustained. I don't owe you any excess of that, because you would be charging me nothing for something; it would be a scam. Islam has a similar position on usury, and is usually a little stricter about it, depending of course on the school. For example, there are a number of Islamic banks today that make interest voluntary; there is just imense social pressure to tip well, and these banks often do quite well actually.
I've wondered about this for so long. I've always guessed that e^x was intentionally created as a means to have a function that equals its own derivative
Another application of the logarithm not mentioned here is the well-tempered musical scale. Interesting coincidence that the invention of this scale was contemporary with invention of the logarithm.
duude m not into this thing at all, math makes my head spine ! but ooh i reaaally enjoyed this video ! your voice, storytelling, and handwriting are soo calming and satisfying !
Awesome video Mr. Rubin, can you do how people came up with the Fourier series next? I know how to compute the coefficient and use them in differential equations, but I would like to know how we can come up with Fourier series assuming we have no prior knowledge about it.
Thanks! I'll definitely have some things to say about Fourier series eventually. Their invention is a better-known story. Preview: Although you can point to things like the theory of epicycles as a proto-trigonometric series, Fourier deserves credit for the idea that every periodic function can be represented as an infinite trigonometric series. He was trying to solve the heat equation in a finite interval, and managed to find a non-trivial cosine series on (-pi/2,pi/2) to represent a constant. In his original paper, I believe he did not yet have the idea of integrating and exploiting orthogonality to find the coefficients, and he instead set up a not so rigorous infinite linear system to equate coefficients of Taylor series.
Have not watched this video yet , but I certainly will. This is wonderful subject! A few years ago I read the book "e The Story of a Number" I highly recommend this book. Everyone that is interested in math even at the algebra level should know what is natural about the natural logarithm base. Of course the natural log base is critical to the study of calculus. Looking forward to watching this video. Thanks in advance!
Not humanity, but only a few ten thousands mathematicians, philosophers, and scholars. In modern time humanity also does not have so high level math. The majority of people, maybe 97% of people do not know this. Only professors and good students know it.
Please take a look at “The Cultural Foundations of Mathematics” by Professor CK Raju. It is viewable as a Google book. The Fibonacci series was actually found by Hemchandra when he tried to solve a Sanskrit music problem of metering. Sin is actually a howler for the Sanskrit Jya which means a cord in a circle. Jya got mistranslated by the Arabs as Jeb(pocket). Jeb got translated to Sinus and that is how you have Sin theta.
Thanks, great research and presentation. Although I didn't follow everything thoroughly. Did you only use resources in the references or are there any other source?
I'm always happy when I hear someone mention usury these days, especially in a practical historical context. There are many good reasons why it was considered a sin for the longest time, which seem to have been forgotten by our modern societies.
So, *that's* why ln is sometimes refered to (in Spanish, anyway) as Napier's logarithm. I was privilaged enough to learn how to use tables of logarithms for calculations.
I could not make it past the part talking about ancient Sumerian banker. That is fine and interesting and all, but probably should have been another video all to itself. I tuned in hoping to hear about the history and origin of exponent and log function. A small blurb about how they have their origins in ancient banking and compound interest (see video linked in the description!) would have sufficed. Just my two cents.
Really interesting. I've been interested in how one might 'build up' mathematics 'from scratch' if, say, all the world's knowledge but a few 'foundational' texts were to be wiped out some day. Thus, understanding how one might build various math tables, but especially the principles and techniques behind them (i.e. how to actually compute the logs in an efficient way), is always of interest to me. This is not a critique, but more of a suggestion: While I appreciate how much friggin' info you've managed to cram into this video, I must admit that I actually had to play a large portion of it at 0.75x speed just so I could follow along! 😅 Also, there were several (and I mean several!) places in the video where you cover a topic so quickly -- I'm sure a fellow mathematician wouldn't have trouble with it, but I'm not such a mathematician! 😅 -- that I could imagine an entire video presentation on just that one topic that by itself would be very worthwhile (IMHO) and could take up minimum 10 minutes on its own, if only just presented at a slower pace and 'spelling out' a few more of the details. Perhaps it might be worth your consideration to make some videos that go at a more pedagogical pace for a broader audience of math-interested lay people. Two excellent channels that I'm sure you've heard of are Mathologer and 3blue1brown. Mathologer in particular is able to tackle pretty math-heavy topics yet at a pace that a fairly broad audience can still handle. Of course, they use animations, and I'm not asking for that; just for the overall pacing. For example, I imagine that this one 33 minute video could probably be expanded into at least 5 or 6 'episodes' or 'parts' on this one topic and/or sub-topics, and each such video somewhere in the neighbourhood of 10-20 minutes at a more casual pace. Again, this is just a suggestion. It may take more time to make such videos (but then again, if it's more leisurely, and there's less pressure to 'fit everything in', then maybe it might actually take less time?), so I'd absolutely understand if that's not a direction you'd like to go in. Just an idea! 😊
Yes I also think it's very important to know how to build up math from scratch, it's the only sensible way math should be explained in my opinion. Knowing where a certain piece of knowledge comes from is even more important than the piece of knowledge itself. Unfortunately almost noone adopts this approach, people want to skip ahead to the "good" part and often give circular arguments, or derivation using more complicated theory that may even depend on the truthfulness of the fact they're trying to explain itself. One thing I've learned while studying maths is that understanding the whole tree of axioms and proofs that lead up to a fact, that you use as a given, is one of the most valuable thing you can have, contrary to what 99% of people(mathematicians included) might say.
Thanks for the high praise! I'm not a historian, just someone with some specific questions about how and why certain things happened, especially within math, and I just put together what I found into a kind of story that satisfied me. Real history should probably be more careful and complete.
Yes, thought this might be solved very quickly with a novel solution, though on second thought ,worked through the Solution using the quadratic formula and Logs. Thankyou for the video.
Great video. I noticed that your markers are bleeding through the paper to the one beneath it. I have the same problem as I use many colored sharpies for drawing or other things. What I did was take a sheet of cardboard from the back of one of those lined notepads that don't have a cover and the pages flip up instead of to the left, I put that cardboard sheet underneath the sheet of paper I'm working on to avoid ruining the sheet(s) below it. I noticed that you often flip the underneath page over a lot, I'm assuming that's because of the ink bleeding onto the sheet. I could be wrong, just what I'm assuming based on what I see. If I am correct then I hope this tip helps you out a little bit. If I'm wrong, then I apologize for the misunderstanding. Peace out and keep up the excellent work!
Through the years, I have bought some great books about history of mathematics. Some of them I remember being about great men who advanced math knowledge. Some on the other hand were more tuned to math itself. Too bad, I now could locate only one of the history tuned ones, Davis & Hersh: The Mathematical Experience. All my presently on-hand books are more about newer math tables and functions. However, somewhere I still have a book with a title something like "Personalities in Math", just don't remember where. But as a side note, I used to have two slide rules, one pocket size and another longer one for more challenging calculation that I kept in my briefcase. Then came the pocket calculator years. But a couple of years ago I found on eBay another 12 inch slide rule and bought it. It is now within easy reach on top of my desktop PC. Loop closed...
11:23 Hold up these dice are not identical On the left dice the two is on the left and the three is on the right So when you turn it around 180 degrees since opposite sides add to seven, four should be on the right and five should be on the left. However on the right dice the four is on the left and the five is on the right and the dice hasn't been flipped because the one is still facing up
My understanding is that Napier's book had 90 pages of tables with 30 entrees per page, or 2700 entrees total. That would be 45 degrees starting from 90. From 45 degrees to 0 would be redundant information.
Very nice video. Thank you. I am sorry to say that I saw an often made mistake. The map of mercator is cilindrical, but not central. That wold lead to a growth of the lattitude proportional to \tan(\phi), actually the lattitudes, in order to strech a loxodrome to a strait line, is to be proportional to \log(\tan(\phi+\pi/4)). So the projection is non-geometric, Gerard Mercator did not used logarithms, he probable used a paper globe.
The only problem I have with the presentation of this video is that I can't follow along well due to the writing not exactly syncing with the voice. I understand that it takes a fair bit of extra planning and organization, but it'd be nice. otherwise this was a great vid, so much info, I was expecting it to only focus on the actual discovery, but I loved the speculation of how it could've happened
You're right, I have to be more careful about matching the writing with the voiceover. Glad you appreciate the "how it could've happened" parts. I was just curious about where exp and log might first appear to people, and I tried to find out why these other ways didn't happen first.
2:20 - Simple interest (linear growth) could be good enough for early incentives. It's not until people start taking advantage of that system, that a faster system of growth would need to be invented. Maybe the more stubborn clients are just told, "you'll owe me double this time next year."
7:45 - "Rate is now approximately linear", since we are now starting to reach carrying capacity again, and will end up on the top-half of the logistic (sigmoid) function, until we find another way to boost carrying capacity again.
Hello Daniel, Watching your video made me realize how dumb I am and what extraordinary talent you are. I'm just jealous of your brain. Exceptional work. Thanks
We are considering a model where the drag force on an object is proportional to its velocity. The coefficient will take care of the change in units between force and velocity.
![The Most Useful Curve in Mathematics [Logarithms]](/img/n.gif)
I forgot to mention the Fibonacci sequence! Leonardo of Pisa (Fibonacci) described the sequence F(0)=0, F(1)=1, F(n+1) = F(n) + F(n-1) in his book _Liber Abaci_ from 1202 in the context of a word problem about the breeding of rabbits. The sequence was known in Indian mathematics centuries earlier. The sequence does grow exponentially, but the formula F(n) = 1/Sqrt(5) (((1+Sqrt(5))/2)^n - ((1-Sqrt(5))/2)^n) was only written down in 1843 by Binet.
The so called Golden ratio. Actually it should be called Natural or Circular ratio, because it is related to the real value of π (natural value).
@@PASHKULI ...? no, it is not?
@@glowson3844 Just look for inscribed n-grams in a circle, understand the concept behind finding √x geometrically and you will understand why π and φ are directly related. Today we still use the linear approximation of π, which disregards the very small arc cuts, which contribute to the circum. and area. Hence π (the real, natural value) is just a tad larger.
This is very important for astronomy and later will be for discovering dimensions.
You haven't mentioned the contribution of Ibn Hamza al-Maghribi who used logarithm functions long before John Napier.
@@fslurrehman True, but since the late medieval times (western) Europeans (brits, french, spanish, dutch) were the most "expansive" (means conquering) people, thus they took all the credits for "inventions". Iven the battery was invented in Mesopotamia\Iraq... but that is a different subject.
I loved this! Some more history of math should be taught in high school when introducing concepts, we take for granted a lot of impactful work that really had centuries of refinement and adjustement that now seems given by definition on a blackboard that has no relation to reality.
Absolutely!
Exactly.. this way of methodology of teaching should be encouraged in physics, Chemistry, Literature, Biology as well as Mathematics. It gives spirit and enthusiasm to learn more about the subject. It will add value to what the teachers trying to convey teaching these formulas or subjects. I have always witnessed in the class asking some of our practical minded classmates “what all these knowledge will do good in my real life?” With the traditional teaching method we think that the knowledge we have been learning is to get high grades to be better than our classmates and to be excepted to better universities racing and succeeding in tests or exams in front of them. This kills the thirst for knowledge and thirst to try to do better than what is thought to us in school..
No way
And some history of history should be reduced
Way to overcomplicatean issue.
People have always been so smart. These origin stories are fascinating.
AMEN!
When there is a problem everybody needs to solve, people will find amazing solutions that look impossible at a first glance.
I find that education system in most advanced countries are lacking on creativity, which I think it really impacts children to think of new ideas.
Yes people have always been smart enough to screw others with compound interests, and then smart enough to outlaw compound interests because they destroy common folks.
@@gelinrefira all interest is compound interest. It just describes how interest works over time. For example, you have 100$ in saving account with a 3% interest rate yearly. After one year you have 103 (3% of 100$ = 3 more dollars). After year 2 you don't have 106$, you have 106.09$ (3% of balance 103 = 3.09 more dollars). No one "invented compound interest". People came up with interest to get some money back on money they've loaned out. The math just describes how this accumulates over time. You are able to benefit from interest or compound interest just as much as anyone else. If you have a bank account you're benefitting from compound interest. If you have a single stock you're benefitting from compound interest (so long as you chose a good stock whose value goes up over time)
@@gelinrefira non-compound interest isn’t used outside of math.
Since I last studied math for engineering about 45 years ago I had a very hard time keeping up with this video but I still find it fascinating that people were able and willing to produce such complicated work hundreds of years ago. I often wondered how and where all the log tables came from. I think I was one of the last engineering classes that used the slide rule for some of our classes.
Daniel this is amazing. I will have to watch it many times to process everything. Thanks for taking the time to create this.
Glad you enjoyed it!
Absolutely LOVE the history weaved throughout. Amazing, amazing video. Please do more - you have a gift for mathematical story telling. There are more and more people coming who speak the language of math - and this quality of video raises the bar. Reach out.
Thank you! Will do!
When I asked my math teacher where did these magical logarithm numbers come from, she said they are from the back of the math book.
I’m sorry you had a shitty math teacher; math is humanity’s most beautiful / important creation, and it’s truly a tragedy that more people don’t appreciate it.
@@justinwatson1510 while I never did very well with other parts of the math curriculum, I did find an almost mystical fascination with geometry, so much so that I finished the whole years worth of geometry in six weeks. Occasionally I wish I had a similar experience with algebra. Maybe I will in my next life.
I had the exact opposite experience; I sucked at geometry in high school (I blame the shitty Georgia public school partly; the teacher was almost worse than useless) but algebra just made intuitive sense to me. I wasn’t able to appreciate geometry until after I got through differential equations or maybe linear algebra.
you act like its the teachers job to teach you that... they are there to see if you pass exams, stop being ungrateful. and people like you say stuff like "college should be free". education is not free stop whining
😂
I don't get to learn about this part of math, the historical part, in school but it gives me so much more vigour and interest in mathematics. Thank you
Greetings from the U.K....Thank you for this... as a layperson interested in maths, all to often actually uses and examples are not talked about and even rarer the historical background to mathematical concepts... this helps immensely! Though I must say that even now, fifty years after leaving school I’m still waiting for that moment when a knowledge of trigonometry will save my life, as I was constantly told it would!
Glad it was helpful!
When Math was taught to me...Nobody paid much attention to...or even talked about the history. Great Stuff.
History, math, economics, and physics in one video. I love it
+ 1
I believe math should be learned based on problems that need to be solved, rather than blindly memorizing formulas. So, to solve a specific problem, you'd try out many different methods with increasing sophistication, by first using the method used in the stone age, then with the method used in the year 1600, etc, until you arrive at the most efficient/advanced method, which also provides the correct answer. This way you acquire real knowledge and understanding of what you're doing.
But then, you would have to learn trig. before algebra. Good luck with that. I suppose it could be done. It would be interesting to learn how to solve things by numerical methods first now that computers are available to us.
math should not be studied for a particular purpose rather it should be accepted as a form of art
@@ecavero1 That's true. Numerical methods are the way to go for basically all of math taught in schools and colleges. Its easier for us to think about and understand discrete rather than continuous sets. Who the hell knows what infinity means anyway -- e.g. limit goes to infinity? Give me a break. Math needs to be reformulated.
@@ecavero1 you need the math foundations to do it, im helping someone with a project on calculations for a rocket launch to orbit and ISS but everything is a struggle because they lack that foundation.
@@theremin_monkey limits are literally so usefull though. and you cant brute force simulate everything. even with supercomputers you cant (or it would benefit alot from a hybrid approach).
Came across this gem today.
I cannot express enough, how fascinating these contents are .
Thanks a lot
Glad you enjoy it!
@ Daniel Rubin: what a fantastic 30 mins. I can appreciate the amt. of research and hard work that has gone into this.
I have History of Science and math integrated into my STEM course for school students and 2 days are devoted to this entire subject (devoted to relationship between e and compound interest; the need for logarithms etc. ). this video has given me a refreshingly new perspective to make the class more enjoyable.
Thanks a ton for this video
Thanks! Glad to be helpful to teachers
History of such kind is so rare...please keep uploading more videos like these...
Love from Bangladesh 🖤🖤🖤🇧🇩
This is phenomenal. Im glad the algorithm graced me with your channel
Glad to hear it!
This is such an important video. I mean the historical context in which the maths was developed really helps one understand in which other contexts they are applicable.
Thanks, Jaco! That's a big part of why I made this video.
@@DanielRubin1 no, thank you! It's because of this video that a^x=e^xlna isn't just another identity in a long anxiety inducing list of identities that I need to memorise and hope to recognise out of a pile of problems, but now I GET it. This has helped for topics in my applied maths AND pure maths courses
Interesting fact is at 11:25 the dice that you drew were illegal dice. A fact of standard dice is that opposite sides must add to 7. If you rotate one of the dice through what would presumably be the z axis, then you would have one side adding to 6 and the other adding to 8. This was not a criticism of your excellent video but an interesting piece of knowledge that I wanted to share.
oooo cool fact
Fascinating summary. Great idea that the need to record the earliest financial transactions drove the development of writing. Thanks.
Hello from Adelaide, South Australia. I came here for the maths, but the history is just as interesting, thanks.
Glad you enjoyed it
Your sir, have impeccable hand writing. Haven't even watched the whole video, but just had to say it!
Oh it feels like a eternity passed by since the last video I saw. Good to see you.
I actually have a slide rule collection. 😅 I find them superior to electronic calculators in many ways, especially when the slide rule is specialized to perform a specific job. There are slide rules out there specifically designed to compute the frequency of resonant circuits, perform dead reckoning navigation, convert between Imperial and Metric...
Glad I stumbled across this. Math is great. I took many years of math courses at university.
Math history, however, is _chef's kiss_
Just want to say I understood nearly none of this (made it through Calc B but that’s it) but watched the whole thing because of how engaging of a speaker you are, and what a great history lesson too!
Thanks!
That's awesome, Scott Minott! You are the first person to donate to this channel! So grateful!
👏
All abstract concepts should be taught with anchors to historic or social context, this was great. Instant subscribe.
Amazingly in depth, thank you for this resource.
Glad you enjoyed it!
On the question of usury, it's a bit more complicated than that. Merely having Interest on loans was not condemned as usury by basically anybody; Rome had simple interest, and this wasn't completely outlawed even with the conversion of the Empire, or in the Byzantine period.
The classical definition of usury for Catholics is charging interest either with what is known as an intrinisic title to interest, or charging interest in excess of any extrinsic title to interest.
An intrinsic title would be built into the loan: I give you $1000, and insist you now owe me $2000, without any need for me to do any work or sustain any costs to deserve it.
Extrinsic titles would be where you factor in stuff like the work I need to do to loan you the money, paperwork, paying for collection, and later on stuff like lost opportunity costs, inflation, lawyers to write up contracts, etc.
The basic moral premise here is that the quid and the quo in a quid pro quo need to be equal, but in different modes; I pay you, the loaner, in accordance with the value of the service you provide, factoring in the work you did, and the costs you sustained. I don't owe you any excess of that, because you would be charging me nothing for something; it would be a scam.
Islam has a similar position on usury, and is usually a little stricter about it, depending of course on the school. For example, there are a number of Islamic banks today that make interest voluntary; there is just imense social pressure to tip well, and these banks often do quite well actually.
History and Math together, what fun. Thanks.
I've wondered about this for so long. I've always guessed that e^x was intentionally created as a means to have a function that equals its own derivative
Love the history, knowledge is endlessly vast.
Another application of the logarithm not mentioned here is the well-tempered musical scale. Interesting coincidence that the invention of this scale was contemporary with invention of the logarithm.
Please, make a video about that for us if you know the theory, it sounds really interesting.
8:26 ok, the handwriting is amazing, but that straight line with perfectly delineated tick marks for Galileo's inclined plane was truly next level.
You're doing an awesome work, it's really pleasent to watch :).
Thank you very much!
duude m not into this thing at all, math makes my head spine ! but ooh i reaaally enjoyed this video ! your voice, storytelling, and handwriting are soo calming and satisfying !
That was fascinating! It is amazing all the variations on techniques that came before whats is taught today.
Awesome video Mr. Rubin, can you do how people came up with the Fourier series next? I know how to compute the coefficient and use them in differential equations, but I would like to know how we can come up with Fourier series assuming we have no prior knowledge about it.
Thanks! I'll definitely have some things to say about Fourier series eventually. Their invention is a better-known story. Preview: Although you can point to things like the theory of epicycles as a proto-trigonometric series, Fourier deserves credit for the idea that every periodic function can be represented as an infinite trigonometric series. He was trying to solve the heat equation in a finite interval, and managed to find a non-trivial cosine series on (-pi/2,pi/2) to represent a constant. In his original paper, I believe he did not yet have the idea of integrating and exploiting orthogonality to find the coefficients, and he instead set up a not so rigorous infinite linear system to equate coefficients of Taylor series.
Have not watched this video yet , but I certainly will. This is wonderful subject! A few years ago I read the book "e The Story of a Number" I highly recommend this book. Everyone that is interested in math even at the algebra level should know what is natural about the natural logarithm base. Of course the natural log base is critical to the study of calculus. Looking forward to watching this video. Thanks in advance!
Very comprehensive explanation. Thanks.
Humanity had so high level math so many thousands years ago its unbelievable to think of it
Not humanity, but only a few ten thousands mathematicians, philosophers, and scholars. In modern time humanity also does not have so high level math. The majority of people, maybe 97% of people do not know this. Only professors and good students know it.
29:00 when calculating these values, was Napier using scrap paper? a chalkboard? I'm not aware that paper was disposable like it is today.
Excellent work and presentation Daniel. I have subscribed.
Greetings from Melbourne Australia
Harry.
Many thanks!
Amazing. Thank you and hope you keep making these types of videos.
Please take a look at “The Cultural Foundations of Mathematics” by Professor CK Raju. It is viewable as a Google book. The Fibonacci series was actually found by Hemchandra when he tried to solve a Sanskrit music problem of metering. Sin is actually a howler for the Sanskrit Jya which means a cord in a circle. Jya got mistranslated by the Arabs as Jeb(pocket). Jeb got translated to Sinus and that is how you have Sin theta.
Thanks, great research and presentation. Although I didn't follow everything thoroughly. Did you only use resources in the references or are there any other source?
Thanks for including references.
Glad they're appreciated! Lots more great material in those books.
I'm always happy when I hear someone mention usury these days, especially in a practical historical context. There are many good reasons why it was considered a sin for the longest time, which seem to have been forgotten by our modern societies.
Such a good high quality video!
How did this video get so little likes? It's amazing! Keep up the awesome work
I was wondering the same thing. Could always use more! Thanks!
Absolutely amazing video!
Glad you enjoyed it!
Awesome video! I love this channel! 💘
I've always loved Dante's visual of the Usurers' circle of hell
Thank you for this great insightful lecture
So, *that's* why ln is sometimes refered to (in Spanish, anyway) as Napier's logarithm.
I was privilaged enough to learn how to use tables of logarithms for calculations.
Useful recap. Never to be used again.
I could not make it past the part talking about ancient Sumerian banker. That is fine and interesting and all, but probably should have been another video all to itself.
I tuned in hoping to hear about the history and origin of exponent and log function. A small blurb about how they have their origins in ancient banking and compound interest (see video linked in the description!) would have sufficed. Just my two cents.
Really interesting. I've been interested in how one might 'build up' mathematics 'from scratch' if, say, all the world's knowledge but a few 'foundational' texts were to be wiped out some day. Thus, understanding how one might build various math tables, but especially the principles and techniques behind them (i.e. how to actually compute the logs in an efficient way), is always of interest to me.
This is not a critique, but more of a suggestion: While I appreciate how much friggin' info you've managed to cram into this video, I must admit that I actually had to play a large portion of it at 0.75x speed just so I could follow along! 😅 Also, there were several (and I mean several!) places in the video where you cover a topic so quickly -- I'm sure a fellow mathematician wouldn't have trouble with it, but I'm not such a mathematician! 😅 -- that I could imagine an entire video presentation on just that one topic that by itself would be very worthwhile (IMHO) and could take up minimum 10 minutes on its own, if only just presented at a slower pace and 'spelling out' a few more of the details.
Perhaps it might be worth your consideration to make some videos that go at a more pedagogical pace for a broader audience of math-interested lay people. Two excellent channels that I'm sure you've heard of are Mathologer and 3blue1brown. Mathologer in particular is able to tackle pretty math-heavy topics yet at a pace that a fairly broad audience can still handle. Of course, they use animations, and I'm not asking for that; just for the overall pacing.
For example, I imagine that this one 33 minute video could probably be expanded into at least 5 or 6 'episodes' or 'parts' on this one topic and/or sub-topics, and each such video somewhere in the neighbourhood of 10-20 minutes at a more casual pace.
Again, this is just a suggestion. It may take more time to make such videos (but then again, if it's more leisurely, and there's less pressure to 'fit everything in', then maybe it might actually take less time?), so I'd absolutely understand if that's not a direction you'd like to go in. Just an idea! 😊
Yes I also think it's very important to know how to build up math from scratch, it's the only sensible way math should be explained in my opinion.
Knowing where a certain piece of knowledge comes from is even more important than the piece of knowledge itself. Unfortunately almost noone adopts this approach, people want to skip ahead to the "good" part and often give circular arguments, or derivation using more complicated theory that may even depend on the truthfulness of the fact they're trying to explain itself.
One thing I've learned while studying maths is that understanding the whole tree of axioms and proofs that lead up to a fact, that you use as a given, is one of the most valuable thing you can have, contrary to what 99% of people(mathematicians included) might say.
Yeah, I stopped trying to follow along.
This is how history should be taught
Thanks for the high praise! I'm not a historian, just someone with some specific questions about how and why certain things happened, especially within math, and I just put together what I found into a kind of story that satisfied me. Real history should probably be more careful and complete.
I wrote that like ten minutes in. By the eighteenth minute I became convinced I had found the best video on TH-cam. Job well done.
Awesome video! Thank you!
Yes, thought this might be solved very quickly with a novel solution, though on second thought ,worked through the Solution using the quadratic formula and Logs. Thankyou for the video.
greatly enjoyed this!
Awesome, thank you!
Great video. I noticed that your markers are bleeding through the paper to the one beneath it. I have the same problem as I use many colored sharpies for drawing or other things. What I did was take a sheet of cardboard from the back of one of those lined notepads that don't have a cover and the pages flip up instead of to the left, I put that cardboard sheet underneath the sheet of paper I'm working on to avoid ruining the sheet(s) below it. I noticed that you often flip the underneath page over a lot, I'm assuming that's because of the ink bleeding onto the sheet. I could be wrong, just what I'm assuming based on what I see. If I am correct then I hope this tip helps you out a little bit. If I'm wrong, then I apologize for the misunderstanding. Peace out and keep up the excellent work!
You're right, my markers do bleed through. Still looking for better ways to do these videos. Will try the cardboard.
Could you let us know which source says ~8000 BCE for banking.
Shouldnt it be (35/36)^(n-1) rather than ^n? For the snake eyes dice problem.
Through the years, I have bought some great books about history of mathematics. Some of them I remember being about great men who advanced math knowledge. Some on the other hand were more tuned to math itself. Too bad, I now could locate only one of the history tuned ones, Davis & Hersh: The Mathematical Experience. All my presently on-hand books are more about newer math tables and functions. However, somewhere I still have a book with a title something like "Personalities in Math", just don't remember where. But as a side note, I used to have two slide rules, one pocket size and another longer one for more challenging calculation that I kept in my briefcase. Then came the pocket calculator years. But a couple of years ago I found on eBay another 12 inch slide rule and bought it. It is now within easy reach on top of my desktop PC. Loop closed...
Thanks man. I am from India , not good English but still easy to understand your English accent.
fantastic video, thanks for making it!
This is amazing, Thank you !
Glad you like it!
11:23
Hold up these dice are not identical
On the left dice the two is on the left and the three is on the right
So when you turn it around 180 degrees since opposite sides add to seven, four should be on the right and five should be on the left.
However on the right dice the four is on the left and the five is on the right and the dice hasn't been flipped because the one is still facing up
6:35 if you want to know more about the ancient economy i highly recommend "Debt: The First 5000 Years" by David Graeber.
Nice presentation, and nice handwriting!
11:39 you painted the dice wrong. The opposite sides always have to add to 7
THANK YOU ! 👌
Have you had a chance to do a video on Lambert's W function?
I had to look it up. I've never used that function. Do you use it for something?
Great analysis
Perfect handwriting there .. impressive
Please do a video on old school celestial navigation
My understanding is that Napier's book had 90 pages of tables with 30 entrees per page, or 2700 entrees total. That would be 45 degrees starting from 90. From 45 degrees to 0 would be redundant information.
Impressive, very nice.
Glad you like it!
Very nice video. Thank you. I am sorry to say that I saw an often made mistake. The map of mercator is cilindrical, but not central. That wold lead to a growth of the lattitude proportional to \tan(\phi), actually the lattitudes, in order to strech a loxodrome to a strait line, is to be proportional to \log(\tan(\phi+\pi/4)). So the projection is non-geometric, Gerard Mercator did not used logarithms, he probable used a paper globe.
This is knowledge explosion!
11:20 Assuming both dice are Identical
They are incorrectly drawn
The only problem I have with the presentation of this video is that I can't follow along well due to the writing not exactly syncing with the voice. I understand that it takes a fair bit of extra planning and organization, but it'd be nice. otherwise this was a great vid, so much info, I was expecting it to only focus on the actual discovery, but I loved the speculation of how it could've happened
You're right, I have to be more careful about matching the writing with the voiceover. Glad you appreciate the "how it could've happened" parts. I was just curious about where exp and log might first appear to people, and I tried to find out why these other ways didn't happen first.
So you can calculate the amount of time to get from anorganic to organic to live? Very interesting 😮
Interesting. Animals that store food are banking. I never thought of it that way.
Superb !
Thanks a lot
we learnt how to use log tables and slide rules in the 70s, probably amongst the last kids who did once electronic calculators came on the scene
2:20 - Simple interest (linear growth) could be good enough for early incentives. It's not until people start taking advantage of that system, that a faster system of growth would need to be invented. Maybe the more stubborn clients are just told, "you'll owe me double this time next year."
7:45 - "Rate is now approximately linear", since we are now starting to reach carrying capacity again, and will end up on the top-half of the logistic (sigmoid) function, until we find another way to boost carrying capacity again.
Hello Daniel,
Watching your video made me realize how dumb I am and what extraordinary talent you are. I'm just jealous of your brain. Exceptional work. Thanks
My father used a slide rule in college and I own it now. I learned to use it as a child.
great video! thanks alot
Awesome !
so sumeria was 1 of 109?
fascinating, thank you.
i couldn;t help but notice the two die you drew at ~11.20 are mirror images of each other. i wonder which is "correct"?
Try slowing video speed down to x0.8 us much easier to follow 😀
Wonderful work, now if you could just get James Burke as a narrator.....thanks for what you have produced.
The tedious work that past mathematicians did is outstanding.
Oh wow, your handwriting looks exactly like mine in this video ✍️😋👍
drag force, m(dv/dt) = C(dx/dt)**2, not c(dx/dt) ...?
We are considering a model where the drag force on an object is proportional to its velocity. The coefficient will take care of the change in units between force and velocity.