Logarithms: why do they even exist?
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- Опубликовано: 7 мар 2021
- Hi guys! In this video I chat about the history of logarithms. I know... not the most exciting topic but it turns out they were pretty influential in mathematical history.
Enjoy!
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I'm a product manager trying to understand why our math expert has inserted log base 10 in a formula. I still don't understand that but I understand logs much better than before. Thanks for this!
You're welcome Sam! Glad logs are making more sense to you now.
What's the formula?
@@histrion2 probably a trade secret
How about asking your math expert? I bet he knows.
He probs just wanted to compress datasize in db, number's sizes may be capped depending on which u use
I love mathematical explanations that include historical context. Those help me to understand the purpose behind the tool, and suddenly all feels much more down to earth. Thanks for this awesome content!
You're very welcome, I'm so glad it helped you. Thanks for the lovely comment!
Had a math teacher from the 5th to the 9th grade, that always introduced new contents with the history behind them. Who invented it, when did it started being used, what are the uses in the real world... It captivated the attention of the class and made math a lot more interesting. It went from the most hated class, to a passion that I still have today. She was a great teacher. I actually spent 4 years teaching when I came out of college, and I tried to apply that same method as much as I could.
I'm legitimately shocked that not once was William Oughtred brought up.
The man who single-handedly took the "OP plz nerf" logarithmic property of log(a)+log(b)=log(ab) and used it to create the slide rule.
A computational device so incredibly useful, revolutionary, powerful and groundbreaking, that it was in continued use for over 400 straight years and it took literally the invention of the electronic calculator in the 1970s to finally surpass it.
Logarithms literally put Buzz Aldrin on the moon with his landing calculations that he computed on his Pickett N600-ES Trig Log Log pocket slide rule.
A feat that would have been impossible without Napier's hard work. :D
The "OP plz nerf" property hahah love it! Great addition thank you! The main focus for this video was how logs were invented so I didn't end up talking about the slide rule. Might do another video on that invention alone.
@@ciaranmcevoy9875 The Change of Base formula is also pretty broken, not going to lie.
"Oh, crap! I need to find the log of some strange base but my calculator only supports common log and natural log!"
*Change of Base formula busts in like the Kool-Aid Man*
My school slide rule is my oldest and one of my most valued possessions. Teacher wouldn’t explain the LL exponential scales and they were not at all intuitive to use. I learned how to use all of that slide rule forty years later with the free time approaching my twilight years.
Following your introduction, I asked myself "what kind of oddity am I ?" because I really wanted to know what a logarithm is and what is it used for. I passed all the mathematics courses for a career in mechanical engineering before computers, and even calculators, but never digested the content. Just passed. This video is exactly what I was looking for. It is the amazing minds of the heroes of mathematics that I would like a piece of. Today, computers have left humans without a reason to think, understand and consider applications. No engineer I work with remembers a course taken. They rely on apps with no idea what the app is doing. God help us when the electricity ends. ...Now, off to a video on how to use my fathers slide rule.
Are you aware of why Napier wrote his work in Latin? At that time, Latin was the universal language of educated people. Whether spoken or written, an educated person from one country who did not speak or write the language of another educated person from another country could communicate with that person through Latin. Since Latin was a dead language, it meant that it was unlikely to change. It also meant that if a person wanted to attend a college in another country, he didn't have to learn the language of the country the college was located in. That is why Latin and Greek are stil used in science today.
That's brilliant! Thanks for sharing!
What about pig Latin?
The more I learn about the past the more convinced that we have past a point of inflection in homosapien evolution and are now progressively becoming stupider with respect to time I become.
@@Nivleknosnhoj I agree.
p.s. "past" should be "passed" and I would move "I become" to just after "more convinced".
@@Bapuji42 I'll pass 😆
I am engineering student from india and I really like your reasearch and the way you explain it in a ease. Thanks for such a great video ❤
Logarithms are one of the most amazing mathematical tools that I have come across so far in my studies as an aspiring engineer. Math is used to define and logarithms give us the ability to make definition of that which we usually cannot do algebraically. They can help us to better understand the world around us and give are a tool to precisely find that which we instinctively estimate as human beings. One thing I really love about logarithms is their function in finding the distance between things, measuring parts of a whole, whether it be music, sound, something physical, and so on.
Thanks for sharing your insight Joseph. Great to hear such passion and interest!
Man, I hate math but this one right here has changed by perception. And Laplace's praise got me goosebumps.
Thanx, earned a sub!
I really appreciate that Narendra. Thanks for the lovely comment!
I think you've done a fine job with this. Napier's logarithms and Harrison's clocks are two British ideas that made marine navigation much easier and saved countless lives at sea.
Great video! I finally understood what " Log " is for!!!! plus the background story of how they came about made it interesting and extra easier to kinda grasp.
That's great to hear Melizabeth! Glad you enjoyed the video.
I came into possessive of a book of 7 place logarithms from 1 to 100,000. I’ve used them to convert complicated calculations into nothing but pencil and paper. Also found logarithmic trig functions, they are log+10 to avoid negative numbers.
Love that! Using logs for their original purpose. Nice.
I am a game developer trying to understand where Logarithms fit in this area. It's a pretty interesting topic! I am still struggling to grasp it's pure essence. Something is still missing. But, great video! One of the best I've seen so far.
Well the pure essence of logarithms is that they are the inverse of exponential functions. But that just begs the question: "what is the pure essence of an exponential function?" Maybe these two answers to this question will help you (if you don't already know them):
1) Exponentials are functions that convert addition of their inputs into multiplication of their outputs. To take the inverse, we reverse the input and the output. So the upshot for logarithms is that they are functions that convert multiplication of their inputs to addition of their outputs.
2) Exponentials are functions that grow in proportion to themselves. In other words, the rate of change at some input is just the output of the exponential multiplied by some constant number. Once again, to find the inverse we reverse the input and the output. So the rate of change switches from dy/dx to dx/dy, which is the reciprocal. This means the rate of change of the inverse is some number _divided_ by the output of the exponential. But remember the output of the exponential has become the input of the inverse function! So, the rate of change of a logarithm is simply some number divided by its input.
These two interpretations cover a large portion of the properties of logarithms.
Do you remember learning in school that you can add exponents when you multiply? As in, x^a times x^b is x^(a+b)? Well, that's all logarithms are. If y = b^L, then L is the "base b log" of y. 10 is the most obvious value for b - those are called common logarithms. But there's also a special number called e - those are "natural logarithms." And if you happen to work in computers or information theory you might see 2 used as the base. The whole idea is that this lets you directly exploit the "adding of exponents" to turn multiplication problems into addition problems.
Computers hide the value of this, since it's just as easy to type * as it is to type +. But addition is faster on computers than multiplication, so in the game arena you might find occasional places where considering logarithms might let you produce faster code.
Thank you. I appreciate the time you took to explain this and the beauty of the history.
Thanks Ciaran! You've added a lot of fascinating history of these peculiar functions. I love it!
Cheers Tommie, I appreciate that pal.
Fantastic video! It was super engaging, well-researched and just lovely to watch. This is no small feat with a subject as potentially dry as logarithms, but you made it come to life like few ever could. Hats off to you sir 👍🏼😊
Thanks very much Fernando. What a lovely compliment. I appreciate you acknowledging the difficulty of the subject, so it really is great to know that it came across that well. Thanks again pal 🍻
This is great and I appreciate you sir! Well put!
Thanks Alex. Glad you enjoyed the video.
Wonderful job. Thank you! I will share with my students.
Very interesting and well presented in a clear voiced…subscribed!
Great to hear pal! Glad you enjoyed it.
This was so helpful in conceptualising a concept which has been challenging to grasp. Thank you!
That's so good to hear!!
I REALLY enjoyed the video! Great work
Thanks pal!
Fascinating. I never knew their basis or history. I understand them much better now. Thank you!
You're welcome Ron. Glad you enjoyed the video!
It might have been tough to research and write maybe, but the way you convey it to the audience is even more impressive considering you do it like a conversation or a stand--up. Great video.
Thanks pal. That's very kind of you to say.
Thanks , for explaining the work of such great mathematicians , who have shaped today our generations with their work , in an enjoyable way, hope your efforts get recognized and cheers.🎉🎉
Thanks Anish! It's much appreciated, I'm glad you enjoyed it!
I enjoyed watching this video. Very fun and enlightening! Cheers!
That's lovely to hear Jewell!
I absolutely loved this!
Applications are what is so fascinating and practical:
Can you do a video on the logarithmic relationship between additional units of tnt and the explosion (energy release) that results when detonation takes place?
I love the history behind logs, fascinating!
This is great. It didn't fully click when watching other videos. I understood how it works, but I didn't understand why was it created in the first place and its application.
Thank you for that great approach of teaching the Logarithmen and thank you for leaving out to many confusing equations ❤
what a delightful explanation of why our perception of time changes as we get older, thanks.l
I am not a mathematician. I am just a self taught software developer who is struggling though a computer science course. One concept I keep running into is logarithms. Finding information on how to use them has been straightforward, but felt like only half the story. I wanted to know why they were even a concept. I knew they were useful, but I did not know what problem it was meant to solve. It felt like they only existed just for the sake of being esoteric so problems could be solved in a specific way. To my mind they were a solution searching for a problem. It just felt like an alternate way to write exponential equations. Your video does a wonderful job at starting to help me understand they are indeed vital to understand and not needlessly esoteric at all. Thank you!
That's great to hear pal. Glad it helped!
While I still can't say that I truly understand the application of logs, this video cleared up much and I can honestly say I like logs a lot better than I have before. Thank you.
But what exactly is a logarithim? What does it do to the number, I don't quite understand still. How did they figure out how to use logarithims, how does it modify the number? I'm deeply confused, but highly intrigued!
Great video! Thank you!
Historical context helps a ton!
Logs are still super important in computation. Lots of computations are done on log scale and only turned back to normal scale at the end. If you don't, you frequently overflow the computer and can induce other numerical issues. As an example, if you work with the gamma function, chances are very good that it's actually represented internally as the log-gamma function because otherwise the numbers get so large you can't store them anymore.
Great insight, I love it! Thanks pal.
Really great video!
We definitely appreciate the effort Your Excellency. Please keep them coming.
Thanks Shravan, I definitely will do.
What a fantastic video! I enjoyed watching it.
Thanks Olayinka, what a great compliment!
Thank you! Taking on the task of preparing and teaching about logs proves you have a lot of stamina. Use that while you have your youth and I will look forward to more lessons. A note: I once told an experienced engineer (who was always somehow confused by logarithms) Repeat, to yourself, “A logarithm is an exponent.” (of a base.) After that he was confused no longer.
Thanks Zack!
Great work!
Thanks 👏 the humour works too btw.
Enjoyed the history and the problems. Subscribed too.
Thanks pal that's lovely to hear
I appreciate and admire your benevolence.
Thanks for your work :)
Interesting video! Thanks.
This video was fun and Intresting !
Loved his sense of humor.😆
Thank you. That's lovely to hear.
The years being just as long as they ever were is exactly what I needed to hear. Thank you!
Hey simyshell, glad you found some comfort in it, as did I.
Thanks for this good video you deserve a bigger audience
Great video!
... A good day to you Ciaran, What I can't get out of my brain about logs is: the log of a given number (argument) is that exponent by which one has to raise the base of the log to get the given number back; in short, the outcome of a log is an exponent! I always use as the example the very practical Richter Scale ( large earthquake energies represented by simple numbers ). But just to be on the safe side, I regularly briefly repeat the theory about logs, in order to be able to continue to manipulate them efficiently (lol). Your presentation increases admiration and respect for this indispensable math topic! Thank you very much for your interesting math efforts ... Jan-W
Hey Jan, thanks for the lovely comment. I personally believe logarithms get lost, just as you've pointed out, from their purpose (mainly due to their name I'd say). It's forgotten that they go hand in hand with exponents. They allow you to move your mathematical efforts into the exponent space of numbers.
Finally, a mathematician that speaks coherently. Subscribed.
That's great to hear pal!
@@ciaranmcevoy9875 I meant to say something along the line of you are aware of the meaning of what you are saying. That comes through to your audience.
Thanks pal, I appreciate that.
that was a really good video, helped me find out the history of logarithms
Glad it delivered Tarek :)
thanks for your persistence
woww excellent content brother 🙇
Well done, thank you.
I'm doing my alevels and your vids are making so much sense of what i study
That's so nice to hear pal! Makes them worth doing 👌
I lole yhat you gave burghi due credit...the meeting of napier and briggs is a classic demonstration of the scientific method at work, in spirit and indeed
You know, I did not believe you when you said I might even start to like logarithms by the end of the video. Well, I have successfully been proven wrong 😂Thank you so much for this! You had me hooked the whole video (plus I love your sense of humour tactfully sprinkled in) and made a topic I hate so interesting. Fascinating story, huge respect for John Napier and the others. Just wow
Haha that's brilliant to hear pal! Thanks for the lovely compliment.
Great job!
Lovely video !!
Well, this is a diamond in the rough, thank you. Helped me to understand logarithms when I know where they come from
This is great to hear Zorski. Glad the video helped.
Your vids are amazing
Simply joining the thanks. Very clearly put. Please carry on
Cheers pal! I definitely will carry on.
Thanks for demystifying the Math and making it fun. Cheers 🍻
Good video, thank you!
one more feature you didn't mention is floating point numbers in computers - these numbers are stored in binary scientific notation, which is about 80% of the way to a logarithm, and forms the basis of most of our critical multiplication operations
Love this! Great addition!
Definitely I do appreciate your effort. I have read and listened to a lot of resources about history of logarithms, but still l got some new information from your video. So please keep up with your great effort. I hope your channel subscribes Skye rocketing
Thanks for the kind words and good wishes Omar!
Thanks!!
respect to napier, burgie and respect to you as you explained logarithm so that I can understand. Your student should be lucky. Teaching has to be like this
I appreciate that, thanks!
It would be cool to show how the slide rule developed from this since it's just a couple of graduated lines you match up, in fact, its a bit strange that somebody didn't discover logarithms from playing with marking sticks.
Yeah I've had this mentioned a couple of times now. It's definitely on the cards.
Oh my goodness. AMAZING!
Thanks Purple!
Being born in 1962
and was introduced to logs
before I had an electronic calculator
though a friend at school did have a mechanical calculator!
so for me logs were a useful aid
even if I did drop them as soon as in the sixth form
my father bought me a calculator
(with a square root function!)
I possibly had a bigger problem understanding
why I had to learn how to use a slide rule
logs seemed so much more useful and had better accuracy
but my father, who was an engineer,
swore by the slide rule.
Thanks for sharing this John. Yeah, once you had the calculator, I can imagine the accuracy of the slide becoming almost redundant.
@@ciaranmcevoy9875
I only ditched the log book
when I got a calculator
with log ln, e^x and 10^x buttons
It was an electronic log book
that fitted in my pocket.
BTW I did all my mathematics exams
with a ban on calculators.
Though the mathematics at university
was much more problem-solving than
calculation.
Yeah, the use of logarithms to problem solve is where they really shine and calculation only comes in to get the final value (if required). I love the notion of having an electronic log book, I know modern calculators are essentially that and more, but just the simplicity of the progression from paper to digital is rather quaint.
@@ciaranmcevoy9875
If you are brought up with log books with look up tables for log, ln, 10^x and e^x
as well as the trig and hyperbolic functions
Both the teachers and students
use the methodologies of the older method
like the first quantum theories
versus quantum mechanics.
love ur sense of humour
Very I interesting video. Love the history of logarithm
Thanks Reynold!
Blew my mind!
I think it's safe to say many of us feel the reason this topic is often disliked stems from the lack of context in schools and universities. As an engineering graduate, I found myself relearning almost everything independently to truly grasp the subject, rather than just focusing on passing exams. Fortunately, I now have the time to access resources like yours, which were not available when I was in school. Libraries were (and still are) filled with dry, context-lacking textbooks that made learning challenging. In response, I've started teaching to provide a different approach, and it's satisfying to see that everyone can succeed when taught the right way. Your content is truly valuable, and we wish we had more teachers like you.
Your story sounds awfully familiar to mine :) thanks for the lovely comment
Well done!
LETS GOOOO BIG DADDY CIARAN
Log is used nearly everywhere in number theory as, due to be very nature of how base systems work. The number of digits a number has is very very intrinsically tied to its logarithm in that case.
Now we need a video on the w Lambert function!
In school we used log and antilog tables without ever being made aware of the principle behind them. Perhaps it was but we (or maybe I) were/was too young and naturally ignorant to grasp the harder part, this essential cleverness from back hundreds of years earlier.
I like mathematics much more many, many decades later having re-learned much of it out of residual curiosity. With a better insight I could have loved it way back then instead of just enduring the robotic procedures like grinding through some hated language.
Just entering the teenage years of course carried the handicap of emerging laziness and arrogance, the best years and the worst for learning?
I like his explanation, I have met people and worked with people in different trades and different professions people who knew their profession or their trade better than possibly anyone else, than what you could expect any expert in their field could ever accomplish but yet they did not have the gift of knowing how to break it down simple and teach and convey it to others. I have known people in the welding field for example, they were very good welders , but they didn't know how to teach it to others, they would have been some of the worst teachers and would have just turned people off. I think when teaching anything to another person you have to go slow, you can't speak the jargon or the lingo relevant to that field very fast, like you're running a race, and you have to explain every little segment as you go along, because if you go too fast, some people are just gonna get overwhelmed with the lingo that they've never heard before and they're just gonna tune in to some other place hoping that somebody else will be gifted to be able to teach it and break it down so they can learn it more easy , And that's why we see in a lot of our schools , or let's just say, across the nation , that other countries, I think we're 29 on the list of being below other countries when it comes to math knowledge, there are teachers that can teach you math and make you love it but then there are other teachers that try and engage themselves to teach you and make you hate the very thing that you wanted to embark upon. China turns out more engineers and scientists than the USA, they prioritize their students to learn math if nothing else. Some teachers can teach calculus so easy, some other teachers will only further confuse students and make them forsake their major in college that required high grades in calculus, it's so sad that it's like this in the USA, we have to import nuclear physicist from other countries, or the Manhattan project never would had been successful. Teachers at the beginning of the year need to explain to their students first WHY THEY NEED THIS MATH KNOWLEDGE AND HOW IT IS RELEVANT TO THEIR FUTURE CAREER, because many students sit in class daily, bored, asking themselves how is this or knowing it going to help me in life, then they sadly divorce their attention and thoughts from the math lectures being given to them by their teacher daily, and flunk it. Math teachers 3 times a year ought to expound to their students their need to know all math through calculus. But nothing is going to change for the better in this country. When you have a Supreme Court that legitimizes men marrying men and women marrying women, then you have set the stage and advanced a nation to be ripe for the judgment of God, every segment that comprises human life from that point on races forward into perversion and degradation, darkness is upon this land and people, the highest court in the land have shaken their fist at God, as God spoke through the prophet NAHUM, (I will pour abominable filth upon thee), so now we see this in a country that God previously blessed, but no longer, this nation is cursed in the food market and gas pump, and it's going to elevate into cataclysmic horror, when God fights against a nation that backsides from His commandments and laws, believe me, there are no brighter days ahead folks. Start storing food, water, fuel, and all necessities, because the locust storm heading our way will burn up our food supplies, martial law will become the rule of the day, and fear of daily existence will rob people of what peace and contentment they once knew. God is no respector of persons, the very elected leaders that we see daily make and act upon insane drafted policies , designed to steal and rob us of peace, safety, and prosperity, are part of the punishment from God, who is now fighting against a nation that embraces perversion and prosecutes those that are against it. IM NOT A LOOSE CANNON, I'm just reverberating what investigating journalists tell us daily in local and nationwide broadcast, granted the freedom to do so by the constitution of the USA, and the freedom of information act. The truth hurts and offends those that are guilty of violating the principles of wisdom, who seek to walk in their own ways that are destructive to theirselves and others. Back to math knowledge, watch what I proclaim, next year USA students will fall even lower in the nation, a nation that through its court systems have shaken their meager fleshly fist at God and rebelled horribly against Him.
Sir this is a Wendy’s
Who are you man!! I too possess the same thought as that of you, what a Coincidence!!
Awesome introduction. When I tried to reinvent how and why logaritmic rule (it's slide rule in english actually) works, I came to exactly the same image as shown at 6:11. However I sort of wonder how people invented powers of weird numbers, such as 10^0.30103=2 or 2^3.3219 which is 2^(10/30103). I guess there is some method such converting log_b(x) to ln(x)/ln(b) and then using sum of some series and afaik nice square roots are done by repetition of trial-error-qualified correction based on derivation.
I would die for such a humorous and intelligent lad in my life.
you help me fell asleep, I used to visit an alcoholic anonymous group and join a street fight club but finally I found this channel, thaaanks
As a student, who has just begun looking at logarithms, this was very insightful and has made me appreciate logs more than I thought I would.
Leaving a like for the algorithms ;p
That's great to hear pal! And cheers for supporting the channel :)
Great!
Very good video friend i hope your channel get bigger
You have honored your predecessors. Well done Sir.
Certainly u did them justice. Tku much
Logarithms allow the solving of some sticky equations. For instance the radioactive formula. It depends on a log identity. Namely the log to the base a of b raised to the power of c is equal to c times the log to the base a of b. In other words you can put the exponent before the log expression instead of leaving it as an exponent. By the way, the radioactive formula is At = (1/2)(t/h)A0 You can't reproduce exponents and subscrips here so in words: The amount of a radioactive substance at time 't' is equal to one half raised to the 't' divided by h times the amount at time zero where t is the time elapsed and h is the half life of the particular isotope.
I'm neither smart nor intelligent.
I'm not even good at solving mathematical problems, either. But,
Every part of Mathematics is my favorite.
I just love mysteries of Mathematics.
Mad Respect To John Napier For Inventing Logarithms.
I love math. Nice work. It would be interesting to understand how computers calculate log with just binary numbers.
Thanks pal. That would be interesting to know! Might have to look into it...
your video deserved alot alot of likes and subscribers ...
Thanks pal! Nice of you to say that.
Thankyou
do you still have that poster link?
Keep it up🙌
Thanks Sandip, I will do.
Thanks
I'm an OLD GUY. I learned high school science and math before the pocket calculator. Logs made higher math possible. The slide rule ( logarythyms incarnated ) was the greatest tool ever invented.
Cheers Larry, that's so cool to hear!
Appreciate the content! Camera/focus jumps were tripping me out though
Appreciate the feedback Greg. Might ease up on the attention grabbing cuts haha.
Hi Ciaran, is there a philosophy why and how Imaginary numbers exist?
How do you show imaginay number representations, physically?
It's a good question, when imaginary numbers were first discovered they were suggested to be called "lateral" numbers. Because they can be seen to be another dimension to our 1 dimensional number line. In essence, they're not imaginary at all. Might be worth another video :)
@@ciaranmcevoy9875 Thank you.