What was it . Do 18504 equations to prove your hypothesis of finding a cool way to cheat the lack of time and mental capacities of an individual? Some would call those people in their time "ill-logical" - so much effort with the risk of gaining nothing. Let's be honest - those two were just having fun on their 18503rd equation and when they got to 18504, they were like - ohno, I found a way to do less equations.... now I have time for my children.......... I must burn this, but maybe this is not enough to prove what i think I've found - better continue.
This is the best mathematics video I've ever seen..It really makes me interested in mathematics and appreciate the beauty of it..For the first time in life I feel the urge to learn mathematics in depth..thanks for igniting my mind with this amazing video sir..keep making such videos.😁👍🏼
This will probably seem obvious to most but I think it might be useful to point out that the aim of applying a base as small as 1/10,000 was to enable the log application to any number (well, almost). Perhaps it was just me not picking this up when listening. Thanks for sharing.
i was also not weak in maths, i failed to understand the application of it. Thanks to internet and world of technology today you can learn what you couldn't? Thanks to the people who were involved in creating this world of computers.
Tip: if you how many digits are behind the decimal form you can use it to tell you how many digits there at maximum when raiseing the power from the base except, for infinite repeating fractions or irrational numbers. You then have select finite digits of your desired. Example: if 1.0001 has 4 digits behind decimal then if i raise it to the power 2 then its 8 digits. This is useful to keep track of your calucation because you will have a increase certain chance of discovering your missing or short/overshooting maximum digits behind decimals from vast large multiplication.
I must be one of the only ones who didn't fully understand logarithms from this video, but I do like the presentation. Then again, I have a poor understanding of logarithms in general.
Basically logarithm deals with power of a number. Focus more on the example which was based on 10. I think that one will help more to understand what logarithm is.
I was intrigued by the word logarithms, so wanted to know how/why the word “logarithms” was used to describe this. The word “log” means a record, a ledger. “arithms” looks very much like the word arithmetic. It seems that the word {log-arithms} is just a joining of these two root words. Hence the word logarithms simply means a ledger/record/record of some number set.
Actually, the "log" part comes from the Greek word "logos", which the etymology says means "reckoning" but I think it can also mean "word". And "arithmos" means "number". So "logarithms" are "reckoning numbers" or "calculating numbers."
GREAT video! I knew about Napier but not Jost. One person explained logarithms to me this way: A logarithm is the answer to the question: "What power do you raise this number (the base) to, to equal this other number?"
Just for your information. What is falsely called the pascal triangle was in fact discovered by the great Persian mathematician Omar Khayam about 8 centries ago who is better known for his poetry in the west.
Now that we have got all kinds of digital devices, why log of base 10 or e is predominantly used in all of these electronic calculators? Why not introduce log of base 2 for calculating let's just say 5^x = 8?
Aashish Shah the base is really arbitrary. It's just like choosing a coordinate system. I can see how log base 2 would be nice for here specifically because 8 is 2^3, but other than that there is no specific reason to use log base 2 vs log base 10 or anything else
Log2() is popular in computer science for at least two reasons. First it matches the base of the underlying number system, and second a lot of algorithms have log2(n) complexity (usually because they repeatedly halve the problem).
I just did it in Keynote on my Mac. I recorded it in one take (it took several tries to get a good take) talking into the microphone on my ear buds that came with my old iPhone. I'm sorry, this is probably useless to you by now. I need to be better at reviewing comments.
But the point is that Burgi only had to do it once, and then anybody with his table could look up any two numbers in the table (which took up a book), add the logs, and then look up the log to get the product. It really did save time.
One of the points of the video is that there is really no good way to do that for a single number in particular. It's hugely more efficient to build up the table once and for all using methods based on what I described in the video. Power series methods like some computers use are impractical for human computation. There are ways to approach it, but they either involve trial and error or improvisational cleverness. You might look at this link: forum.artofmemory.com/t/calculating-logarithms-by-hand/32855
To get a flavor, just take the ln of both numbers on the left using your calculator. Shift the decimal four to the right and drop what comes after. (That makes your result less accurate but more like Burgi's tables.) Then add the two numbers you just found. To simulate looking up the sum in his table, move the decimal place four to the left and do e^x of that number on your calculator.
Cann't invent any mathematic equation they already exist as part of the fragment of the universe, it can only be discover and rediscover, But all of those parymid and sculpture that exist prove that the ancient already knew this they just didin't name it I guess, but love this presentation.
Sorry, I've gone like a year without going over my comments. What is it that you want me to link to? It seems like it would be redundant to have a link to the video itself.
Well, if you start with 1.0001, then, at the beginning, every time you multiply by 1.0001 it is almost the same as if you just added 1/10,000. But not exactly the same, and the difference gets bigger the more times you do it. So, if you added that amount 10,000 times, you would get exactly to 2. But if you multiplied by 1.0001 10,000 times, you get something close to e. They hadn't invented that name yet, but that's the amount. They understood that you could get more accuracy in your multiplications if you used more decimal places so, if you take 1.000001 to the millionth power and so on, the first few digits still start 2.718, but the later digits get more consistent. It was Leonhard Euler who chose the name "e" in the 1700s, long after Burgi and Napier.
Mark Foskey I just want to see if I’m following you correctly. When you wrote “...every time you multiply by 1.0001 it is almost the same as if you added 1/10,000”. Should the last part be (1+1/10,000)?
Sorry this is so delayed (I think my UA-cam email was getting filtered), but no, I really mean it's almost as if you added 1/10,000. Here's what I mean. If you start with 1, then 1 * (1 + 1/10,000) is exactly 1 + 1/10,000. So multiplying by (1 + 1/10,000) is identical to adding 1/10,000. But when you have a number different from before the times sign, they are not identical. 1.0001 * (1 + 1/10,000) is not exactly the same as 1.0001 + 1/10,000, but they are close.
Hi can you make a video on all such mathematical stuff which is in existence now. It would be great. First please start with why they invented mathematical expectations, derivatives, integrals.
I will try: Any time you invent anything, you are discovering the way to make it or a way to think about it. What Napier and Burgi did feels more like an invention, because they wanted a method for solving a problem, and they created tables of numbers that did the trick. But they were also discovering fundamental mathematical objects that (in a sense) have always existed in Platonic space.
Logarithms are still a hugely important mathematical concept. They are used all the time in mathematics, engineering, physics, and economics. Aashish Shah gave an example of the equation 5^x = 8, which you would use the log function to solve. The purpose that Napier and Burgi had in mind was just the first application.
+Vinay Seth Instead of using log2 you can use the log5, which will then eliminate the 5 out of your equation. 5^x = 8 | log5(...) log5(5^x) = log5(8) | using logA(A^B) = B x = log5(8) So the answer to your question is to take the logarithm to the respective base of a^x instead of some other base. By the way, you could simplify your equation to log2(5) * x = 3, therefore x = 3/log2(5). Since 3 = log2(8), x = log2(8)/log2(5). Using the base change identity we can say x = log5(8), thus our earlier solution. I hope that I could help you. Yours, ZfE
Yes, he wrote a very important book on algebra. The word "algebra" comes from one of the terms in the book (al-jabr, it's in the title), and the word "algorithm" comes from his name. But this video is about logarithms, not algorithms. They are different concepts.
Al Khwarizmi was hugely important. But I think it's algebra and the notion of algorithms that he's responsible for. I don't think he invented logarithms.
I said "notion", in the sense of "idea", not notation. And he is responsible for algorithms, not logarithms. They are different. (Actually, the modern idea of an algorithm is a little broader than what he did, but the word does come from his name.)
6561 is not "sixty-five, sixty-one" as you stated. It is "six thousand, five hundred sixty one". You are trying to make the mathematics easier but you are using incorrect readings. So instead of making things easier you encouraged incorrectness. This negates all that you have done. I dislike it when the standard is set by the ignorant.
![The Most Useful Curve in Mathematics [Logarithms]](http://i.ytimg.com/vi/OjIwCOevUew/mqdefault.jpg)
Respect for people in the early years to do the brute force so no one else has to
What was it . Do 18504 equations to prove your hypothesis of finding a cool way to cheat the lack of time and mental capacities of an individual? Some would call those people in their time "ill-logical" - so much effort with the risk of gaining nothing. Let's be honest - those two were just having fun on their 18503rd equation and when they got to 18504, they were like - ohno, I found a way to do less equations.... now I have time for my children.......... I must burn this, but maybe this is not enough to prove what i think I've found - better continue.
Seriously, all these years and somebody finally explains it in a sensible manner. Thank you!
This is the best mathematics video I've ever seen..It really makes me interested in mathematics and appreciate the beauty of it..For the first time in life I feel the urge to learn mathematics in depth..thanks for igniting my mind with this amazing video sir..keep making such videos.😁👍🏼
Thank you!
This is the best intuitive explanation of logarithms that I have yet seen.
Finally understood how the natural logarithm was invented. Ingenious.
Well, this tempted me to solve some of the complex logarithms.
THANK YOU VERRY MUCH!
Thanks Mr. Mark. Finally the words we should have been taught at school! Great piece of learning.
This will probably seem obvious to most but I think it might be useful to point out that the aim of applying a base as small as 1/10,000 was to enable the log application to any number (well, almost). Perhaps it was just me not picking this up when listening. Thanks for sharing.
Excellent presentation! Critical to the understanding of Logarithms
Everytime I realize I forgot how to solve'em, I come back to this vid, and IT ALWAYS WORKS
great video, I appreciate your effort by doing this!
Well this is the best explanation on youtube so far, thank you very much. God bless ya!
It all makes sense now!! Wow, thanks
He thought me in the best way of logarithms in my student Life
Fantastic video....
Everyone trying to understand the real meaning of logs will found it very interesting
Really helpful I was searching from so many days for these answer ,Thank you very much SIR.
this is just too awesome!!! thanks a ton!!!
Great little background history of logarithms!
This is what I call a " good video " , Thank you
Best video on log I have seen
why no one taught me in this way in school
me too !!why no one taught me in this way in school ????
Because schools are to make you into a mindless drone, not an enlightened person.
I you seek for understanding, you have to find it for yourself.
Well if you're 60+ years old you were taught this. However with the advent of pocket calculators you no longer really need this.
i was also not weak in maths, i failed to understand the application of it. Thanks to internet and world of technology today you can learn what you couldn't? Thanks to the people who were involved in creating this world of computers.
In my time, we had these tables. Actually, you should be thankful they canceled them.
Tip: if you how many digits are behind the decimal form you can use it to tell you how many digits there at maximum when raiseing the power from the base except, for infinite repeating fractions or irrational numbers. You then have select finite digits of your desired. Example: if 1.0001 has 4 digits behind decimal then if i raise it to the power 2 then its 8 digits.
This is useful to keep track of your calucation because you will have a increase certain chance of discovering your missing or short/overshooting maximum digits behind decimals from vast large multiplication.
Just one word... Awesome!
I must be one of the only ones who didn't fully understand logarithms from this video, but I do like the presentation. Then again, I have a poor understanding of logarithms in general.
I didn't u derstood it either
Basically logarithm deals with power of a number. Focus more on the example which was based on 10. I think that one will help more to understand what logarithm is.
Great video thank you very much !
I was intrigued by the word logarithms, so wanted to know how/why the word “logarithms” was used to describe this. The word “log” means a record, a ledger. “arithms” looks very much like the word arithmetic. It seems that the word {log-arithms} is just a joining of these two root words. Hence the word logarithms simply means a ledger/record/record of some number set.
Actually, the "log" part comes from the Greek word "logos", which the etymology says means "reckoning" but I think it can also mean "word". And "arithmos" means "number". So "logarithms" are "reckoning numbers" or "calculating numbers."
GREAT video! I knew about Napier but not Jost. One person explained logarithms to me this way: A logarithm is the answer to the question: "What power do you raise this number (the base) to, to equal this other number?"
Wow, I thought of logarithms in the exact same way as no one else taught me an easier way to see it.
That is a great video! Thanks a lot!
Fantastic!
Did anybody else notice how the numbers on the right column are the pascal's triangle numbers? 2:30
(1+x)^n = 1+ ax + bx^2 +cx^3 + ..... zx^n
These a, b, c, d... are the pascal numbers, because this sequence is used to generate the pascal numbers..
Thomas F yes! I was thinking that too!
Where a b C are combinatorics operator of C0 C1 C2....and so on
Just for your information. What is falsely called the pascal triangle was in fact discovered by the great Persian mathematician Omar Khayam about 8 centries ago who is better known for his poetry in the west.
But for power 6 we see a little change. Instead of being 1.0006006....,it is 1.00060015......
You are so Awesome.
fascinating!
You cleared one of my life time questions.
Very good explanation.
Well done!
Excellent video
Love From India,
MAY GOD GIVE YOU EVERYTHING YOU WANT,THANKS TEACHER
Thank you so much for finally making me understand logarithms
Thank you very much. you really helped alot. i would like to make a video how to use log table.
Great !!! can you post on for Pythagoras theorem
awesome video
Thank you very much
Thank You So much sir.
thanks for information
Quality video.
Very good video
Now I understand logarithms he is a good teacher 😃
Now that we have got all kinds of digital devices, why log of base 10 or e is predominantly used in all of these electronic calculators? Why not introduce log of base 2 for calculating let's just say 5^x = 8?
Aashish Shah because many physics formula and maths formula have the log function in them
+Aashish Shah Could you please explain how to solve 5^x = 8 using logarithms? I got it down to log(base2)5^x=3. What after that?
Vinay Seth @Vinay Seth You need to apply log base 2 on both sides and then the variable x is just the ratio of log(base 2) 3/ log(base 2) 5.
Aashish Shah the base is really arbitrary. It's just like choosing a coordinate system. I can see how log base 2 would be nice for here specifically because 8 is 2^3, but other than that there is no specific reason to use log base 2 vs log base 10 or anything else
Log2() is popular in computer science for at least two reasons. First it matches the base of the underlying number system, and second a lot of algorithms have log2(n) complexity (usually because they repeatedly halve the problem).
which app did you use to create this video?
I just did it in Keynote on my Mac. I recorded it in one take (it took several tries to get a good take) talking into the microphone on my ear buds that came with my old iPhone. I'm sorry, this is probably useless to you by now. I need to be better at reviewing comments.
Thanks
Good video
For me, multilying any 2 numbers each time would be much easier than the crazy multiplication by 1.0001 indefinitely... I'm not yet convinced !
But the point is that Burgi only had to do it once, and then anybody with his table could look up any two numbers in the table (which took up a book), add the logs, and then look up the log to get the product. It really did save time.
How do you calculate logarithms though, without calculators?
One of the points of the video is that there is really no good way to do that for a single number in particular. It's hugely more efficient to build up the table once and for all using methods based on what I described in the video. Power series methods like some computers use are impractical for human computation. There are ways to approach it, but they either involve trial and error or improvisational cleverness. You might look at this link: forum.artofmemory.com/t/calculating-logarithms-by-hand/32855
Can we express 0:42 as the log form?
To get a flavor, just take the ln of both numbers on the left using your calculator. Shift the decimal four to the right and drop what comes after. (That makes your result less accurate but more like Burgi's tables.) Then add the two numbers you just found. To simulate looking up the sum in his table, move the decimal place four to the left and do e^x of that number on your calculator.
the dot that i missed
Cann't invent any mathematic equation they already exist as part of the fragment of the universe, it can only be discover and rediscover, But all of those parymid and sculpture that exist prove that the ancient already knew this they just didin't name it I guess, but love this presentation.
DUDE pls put the link in the description... Other than that, solid vid.
Sorry, I've gone like a year without going over my comments. What is it that you want me to link to? It seems like it would be redundant to have a link to the video itself.
but you never explain at the end *why* they ended up with e?
Well, if you start with 1.0001, then, at the beginning, every time you multiply by 1.0001 it is almost the same as if you just added 1/10,000. But not exactly the same, and the difference gets bigger the more times you do it. So, if you added that amount 10,000 times, you would get exactly to 2. But if you multiplied by 1.0001 10,000 times, you get something close to e. They hadn't invented that name yet, but that's the amount. They understood that you could get more accuracy in your multiplications if you used more decimal places so, if you take 1.000001 to the millionth power and so on, the first few digits still start 2.718, but the later digits get more consistent. It was Leonhard Euler who chose the name "e" in the 1700s, long after Burgi and Napier.
Oh right! that follows from the way e's defined, as (1+1/n)^n as n tends towards infinity. n=10,000 is a pretty good approximation indeed
Mark Foskey I just want to see if I’m following you correctly. When you wrote “...every time you multiply by 1.0001 it is almost the same as if you added 1/10,000”. Should the last part be (1+1/10,000)?
Sorry this is so delayed (I think my UA-cam email was getting filtered), but no, I really mean it's almost as if you added 1/10,000. Here's what I mean. If you start with 1, then 1 * (1 + 1/10,000) is exactly 1 + 1/10,000. So multiplying by (1 + 1/10,000) is identical to adding 1/10,000. But when you have a number different from before the times sign, they are not identical. 1.0001 * (1 + 1/10,000) is not exactly the same as 1.0001 + 1/10,000, but they are close.
A question, why’d you start your list with 0. For me I thought you didn’t start with 0
It ends up working out better that way. I want that number to be the exponent, and so 0 should be next to 1 since (1 + 1/10,000)^0 = 1.
Just solve the question!
Don't make things complicated!
Silly Logarithms^
Hi can you make a video on all such mathematical stuff which is in existence now. It would be great. First please start with why they invented mathematical expectations, derivatives, integrals.
Well, this is just a hobby for me, so don't expect anything comprehensive.
Slide rule
Is no one going to argue about invention/discovery?
I will try: Any time you invent anything, you are discovering the way to make it or a way to think about it. What Napier and Burgi did feels more like an invention, because they wanted a method for solving a problem, and they created tables of numbers that did the trick. But they were also discovering fundamental mathematical objects that (in a sense) have always existed in Platonic space.
Hi I am from India. And I am giving feedback to you .
Your contant is very good but
Please speak slow, that one can understand perfectly
Honestly I was going fast on purpose because I read somewhere that gives it more energy. Maybe I overdid it.
lol numerals are different then numbers.. numerals are repesent absolute calculaton or 0-9 and numbers are amount of numerals
didn't get shit.
If computers were available logarithm at the time of Burgi Logarith did not need to be invented?
Logarithms are still a hugely important mathematical concept. They are used all the time in mathematics, engineering, physics, and economics. Aashish Shah gave an example of the equation 5^x = 8, which you would use the log function to solve. The purpose that Napier and Burgi had in mind was just the first application.
+Mark Foskey Could you please explain how to solve 5^x = 8 using logarithms? I got it down to log(base2)5^x=3. What after that?
Vinay Seth x=base5log 8
+Vinay Seth
Instead of using log2 you can use the log5, which will then eliminate the 5 out of your equation.
5^x = 8 | log5(...)
log5(5^x) = log5(8) | using logA(A^B) = B
x = log5(8)
So the answer to your question is to take the logarithm to the respective base of a^x instead of some other base.
By the way, you could simplify your equation to log2(5) * x = 3, therefore x = 3/log2(5). Since 3 = log2(8), x = log2(8)/log2(5). Using the base change identity we can say x = log5(8), thus our earlier solution.
I hope that I could help you.
Yours,
ZfE
I thought Al Khwarizmi came up with algorithms
This guy has a khazar archive
Yes, he wrote a very important book on algebra. The word "algebra" comes from one of the terms in the book (al-jabr, it's in the title), and the word "algorithm" comes from his name. But this video is about logarithms, not algorithms. They are different concepts.
this explained nothing.
Uh no... al khwarizmi invented it way before the 1600s
Al Khwarizmi was hugely important. But I think it's algebra and the notion of algorithms that he's responsible for. I don't think he invented logarithms.
Mark Foskey how can he create a notation for something he didn't even use?
I said "notion", in the sense of "idea", not notation. And he is responsible for algorithms, not logarithms. They are different. (Actually, the modern idea of an algorithm is a little broader than what he did, but the word does come from his name.)
Mark Foskey right, my bad. I read it wrong.
And he wrote it out longhand. Completion & Balancing -- the basics of algebraic manipulation -- الجبر والمقابلة -- is a treasure.
6561 is not "sixty-five, sixty-one" as you stated. It is "six thousand, five hundred sixty one".
You are trying to make the mathematics easier but you are using incorrect readings. So instead of making things easier you encouraged incorrectness. This negates all that you have done.
I dislike it when the standard is set by the ignorant.
Too wordy. Just get to the point.
first dislike hehehe
Thanks