Thats cool, never thought of it like that although we use it for that a lot. algebra is such a fun subject, im a physicist but took an intro course to abstract algebra (which has actually been usefull especially with permutations and stuff) I sometimes think im actually more of a mathematician hahahah
@@AsiccAP dont remember fully, but I think that an ismorphism between groups is essentially a thing which preserves group structure. That is if there is an isomorphism between two groups they are basically the same group, but with different symbols. But yes, this basically means you need a bijection between elements, but also this bijection should be so that the binary operation is preserved or something like that, bit rusty in algebra hahaha
For anyone who doesn’t know this yet, this is a logarithmic graph. A logarithm is the inverse of an exponent, so the equation 2^3 = 8 is written as log base 2 of 8 = 3. This graph is y = log base 2 of x
I would argue it is better than gymnopedie 1, due to it being more underrated and evoking more direct emotion besides emptiness. Since it isn't used in media as much it is less stale/(over)used.
heard in a steam game which title goes with "on a winter's night, four travelers", the click-n-find game, situated in an express train crossing central asia?
@@tiredlittleautisticdemon621 wtf are you talking about buddy, our generation is just as stupid as others before us. so now we have a calculator, so what? they previous generations inveted it, how does that make us smarter?
@@tiredlittleautisticdemon621 ??? The slide rule is a freaking brilliant invention; it's literally a calculator that was invented before computers existed. If anything, past generations were smarter than we are, since they had to figure everything out for the first time.
Well, it doesn't really matter what the base is the logarithm class of functions still has (most) of the awesome properties of the natural log. Log_2(x) = ln(x)/ln(2) This means that the base 2 logarithm function is just the natural log multiplied by a constant.
@@MK-13337 “the logarithm class of functions still has most of the awesome properties of the natural log”. The example you provided is not specific to the natural log, which is what you were highlighting in your original statement as to having the so-called “awesome properties”. You could’ve chosen a better example which IS specific to the properties of the natural log, like how the derivatives of all exponential functions are the original function times the natural log of the base: F(x)=A^x F’(x)=A^x * ln(A) This is an example where the natural log IS very unique and special, which is something your example did not demonstrate.
@@Aerandir09 In this case, yes, but fun fact! In computer science fields, log is assumed to be log_2. At least, that's how it worked in my algorithmics course last semester. Also, sometimes the base doesn't matter (in asymptotic complexity) but that's unrelated. I got so used to writing ln from maths classes in high school that the swap to writing log in cs classes was a bit jarring!
@@Aerandir09it really depends on your field of study, im mathematics we call it log(x). the inverse function of e^x, i mean you define your different bases only using that..
It is a cool fact about logarithms and the visuals are beautiful But I don't think we should introduce students to logarithms this way, the standard "inverse of power" is still the way
The fact that I immediately recognized the curve as log also explains why this showed up in my youtube feed between a cat short and a Lockpicking Lawyer short
I would say that the most useful "curve" in Mathematics is the straight line, being the graph of a linear function. You can linearise many functions using infintesimal straight lines, thats the basis of calculus, and from that follows the product rule, which is an example of an algebra that projects multiplications to additions. So the straight line is the "mother of most functions" ... and algebras.
They used two of these curves to roughly calculate whether or not the first atomic bomb would cause a catastrophic event wherein the detonation of the bomb would set fire to the atmosphere, turning it into plasma. If the curves were to touch, the Earth would turn into a fireball. Fortunately, the curves didn't touch and, in retrospect, the calculations made no sense.
No way bro said this curve makes a mathematical wormhole turning complex problems to simple ones then proceeds to do the most basic shit on a log2 graph
Just try to listen to the initial few seconds of the short video and then listen to Guala by G-Eazy and Gordo. You will most definitely find it exactly the same. It may also be the case that they took it from the piano piece that you had mentioned in the reply. Thanks though.
@@DTLRR it is the case. It's called using a sample, artists do it all the time. Just because he used it in a song it doesn't mean G-Eazy wrote Gnossienne No. 1
@@TheobaldTheBird Yes that I know of. And I did say that he might have used the sample from the original score. And the reason for my uncertainty was - I was ignorant. Therefore I apologise.
log(a*b) = log(a) + log(b)
Lmao
@@clrkgmii you think this is a joke???
@@clrkgmiiwhat you laughing at
Hahahaha
Congratulations, you actually summed up an entire 50 minute lecture in one single comment lmao
The mathematician would say: The real log-function is an isomorphism between the groups ((0, inf), *) and ((-inf, inf), +)
Thats cool, never thought of it like that although we use it for that a lot. algebra is such a fun subject, im a physicist but took an intro course to abstract algebra (which has actually been usefull especially with permutations and stuff) I sometimes think im actually more of a mathematician hahahah
Yeah but a real mathematician would say wow that is way cool!
What's an isomorphism again? Is it just a bijection with some additional properties?
@@AsiccAP dont remember fully, but I think that an ismorphism between groups is essentially a thing which preserves group structure. That is if there is an isomorphism between two groups they are basically the same group, but with different symbols. But yes, this basically means you need a bijection between elements, but also this bijection should be so that the binary operation is preserved or something like that, bit rusty in algebra hahaha
@@AsiccAPBijection that preserves the operation. So if ab=c in the domain, f(ab)=f(a)f(b)=f(c) in the codomain
For anyone wondering, the music is Eric Satie - Gnossiene No. 1.
Initially did not care at all, see the comment now I care 😤
Great song. Satie life was weird like the melody.
For anyone who doesn’t know this yet, this is a logarithmic graph. A logarithm is the inverse of an exponent, so the equation 2^3 = 8 is written as log base 2 of 8 = 3. This graph is y = log base 2 of x
Thank you sir for your clear explanation of this video, maker of video didn't give much context
Will this be true all along the curve line?
@@YG-kk4ey I would assume it is but irrational exponents are weird and idk much about them
@@culaterit’s part of a longer video
@@skalty9868
Thanks for letting me know, I found it now
That's the best visualization of logarithms I've ever seen.
It’s basically the only visualisation of a logarithm lol
That’s why it’s usually the first visualisation of logarithms you ever see…
😂@@gil4784no kidding 😅
@@gil4784well actually no, this graph only true for logarithm with a base greater tha 1
like a print in eyes❤
You can link the video better in shorts, like how 3b1b does it. Just a tip for the future!
Thanks! Yeah was trying to figure out how to do that.
@@WelchLabsVideo have you tried the description or a comment? Current link isn’t usable on many/most platforms
Gnossienne #1 is such s beautiful piece of music.
I know right!
I would argue it is better than gymnopedie 1, due to it being more underrated and evoking more direct emotion besides emptiness.
Since it isn't used in media as much it is less stale/(over)used.
@@TheStickCollector true, gnosienne definitely deserves more attention, though that would probably lead to it being overused, just like gymnopedie...
heard in a steam game which title goes with "on a winter's night, four travelers", the click-n-find game, situated in an express train crossing central asia?
This is how a sliderule works. (Anyone under 60: "What's a sliderule?") A sliderule was a kind of pre-electronic calculator.
Honestly looking at them I can understand why the world is as fucked up as it is. Past generations were fucking stupid 😂
Thank god I'm 61. I was also going to say the same thing.
@@tiredlittleautisticdemon621 wtf are you talking about buddy,
our generation is just as stupid as others before us.
so now we have a calculator, so what?
they previous generations inveted it,
how does that make us smarter?
@@tiredlittleautisticdemon621 ??? The slide rule is a freaking brilliant invention; it's literally a calculator that was invented before computers existed. If anything, past generations were smarter than we are, since they had to figure everything out for the first time.
2^m × 2^n = 2^(m+n)
No way you tried to tell me with a straight face that log base 2 is more important than the natural log...
Well, it doesn't really matter what the base is the logarithm class of functions still has (most) of the awesome properties of the natural log.
Log_2(x) = ln(x)/ln(2)
This means that the base 2 logarithm function is just the natural log multiplied by a constant.
@@MK-13337this is a property of all logs lol. Log_A(x)=Log_B(x)/Log_B(A)
@@alexloveday6430 What part of my comment made you think I didn't know that?
Easier to say 2 maps to 1 than to say 2 maps to say 2 maps to X where e^x=2
@@MK-13337 “the logarithm class of functions still has most of the awesome properties of the natural log”. The example you provided is not specific to the natural log, which is what you were highlighting in your original statement as to having the so-called “awesome properties”. You could’ve chosen a better example which IS specific to the properties of the natural log, like how the derivatives of all exponential functions are the original function times the natural log of the base:
F(x)=A^x
F’(x)=A^x * ln(A)
This is an example where the natural log IS very unique and special, which is something your example did not demonstrate.
Yes because log(a.b) = log(a) + log(b)
if anyones wondering, the function is:
y = log2(x)
or alternatively
x = 2^y
^y√(x) = 2
Thanks for clarifying this video
or y = log10(x)/log10(2) if the calculator you're using only supports log of base 10
@@polybay
Yes ! Thanks
isnt that just y=logx
Close y = log2(x) [base 2] log with out a base value is implied base 10.
@@Aerandir09 yep
@@Aerandir09 In this case, yes, but fun fact! In computer science fields, log is assumed to be log_2. At least, that's how it worked in my algorithmics course last semester. Also, sometimes the base doesn't matter (in asymptotic complexity) but that's unrelated. I got so used to writing ln from maths classes in high school that the swap to writing log in cs classes was a bit jarring!
@@JazzyMaxine I got my degree in computer science. I'm assuming you are talking about big O of n. We always specified base 2.
@@Aerandir09it really depends on your field of study, im mathematics we call it log(x). the inverse function of e^x, i mean you define your different bases only using that..
Did you know that there is only one log-power curve and all other ones are basically scale models of the original ?
Is this equivalent to any exponent function can be written as an e function?
@@Schoko4crafttechnically it’s not even equivalent it’s just the same relationship reflected in the line y=x as ln(x) is the inverse of e^x.
@@Schoko4craft yea a linear multiple .
by scale model you mean what exactly? I dont see how ln(x)^2 for example is a scaled ln(x). (By scaled I assume you mean a linear multiple?)
he means log a(b) = ln(b)/ln(a), so all logs are scaled natural logs, scaled by 1/ln(a) if a is the base
Logarithms are badass
i hate this graph ,this shit show stability in the converter in my masters project this fffing thing ate my time .
It is a cool fact about logarithms and the visuals are beautiful
But I don't think we should introduce students to logarithms this way, the standard "inverse of power" is still the way
so y= logx?
If anyone is wondering. That plot is the logarithm of base 2.
Soooooo a logarithm…?
Yes but it’s also a good idea to learn using the graph of functions
The fact that I immediately recognized the curve as log also explains why this showed up in my youtube feed between a cat short and a Lockpicking Lawyer short
I would say that the most useful "curve" in Mathematics is the straight line, being the graph of a linear function. You can linearise many functions using infintesimal straight lines, thats the basis of calculus, and from that follows the product rule, which is an example of an algebra that projects multiplications to additions. So the straight line is the "mother of most functions" ... and algebras.
Was hoping for an explanation on the relationship between complex logarithms and trig functions
The erik satie's gnossienne 1 on a math video goes crazy bro
i love that i am doing this for long enough to just know how this curve is supposed to look like by heart
Nice music selection for a math video tho
Wait till bro discovers sliderules.
It's very pretty but the real star is still the "natural" logarithm, right?
in this case i think is log in base 2
@@lucasaband8788yes but the natural log is the most useful, calculus and a lot of other math would be insufferable without it
@@alexloveday6430 yeah, english isnt my native language, so i really didn understood the first comentary
This is my most favourite music. Satie's Gnossienne. ❤
This music is forever associated with the video game "FAITH: The Unholy Trinity" for me now
They used two of these curves to roughly calculate whether or not the first atomic bomb would cause a catastrophic event wherein the detonation of the bomb would set fire to the atmosphere, turning it into plasma. If the curves were to touch, the Earth would turn into a fireball. Fortunately, the curves didn't touch and, in retrospect, the calculations made no sense.
I hate how people over complicate things and make them seem more of a big of a deal
This is how a slide rule works, right?
u gotta have to pry the parabola outta my cold dead hands says the physicist
Satie + math = perfection
As soon as i saw that curve i was like: "logarithm 👍"
After half a year, finally found this short
What's the name of the music?
Gnossienne No. 1 by Erik Satie
What's the piece in the background
What song is this? Where have I heard it?
That's just the graph of log2(x)
If you dont know, this is the base 2 logarithm
log2(x) = y
It's the graph fir logx with the base 2
looks like 3am on election night
I like how it works out this way, but IDK why that would help teach it to kids..
No way bro said this curve makes a mathematical wormhole turning complex problems to simple ones then proceeds to do the most basic shit on a log2 graph
Linear functions be like: are u kidding?
"Line go up!"
Bro discovered logarithm 😂😂
As an engineer i just see a diode curve
"Yeah, it's a curve"
-Me, a genius
That's the curve of genetic evolution
Logarithms is really useful in physics and chemistry
Music name?
Gnossienne no 1
Music from Hello charlotte ep 2 OST
I'm curious if that's also a brachiostome curve?
no its a log curve
Whats the songs name?
i dont know but it plays on the queens gambit show
@@lukaswyllis5958 youre right. shazam didnt help me either. its so pleasing. i still havent figured it out. if i do ill let you know
A high school student class who is not a bad at math know this is a lnx graph
Natural logarithm moment.
What is this serene ahh music bro
It's by Eric Satie, sounds like one of the Gymnopedies
@@sweeflyboy Thanks for the sauce 🙏🏻
@@heetgorakhiya2242 No probs :)
Could you post link to full video here please?
ruclips.net/video/OjIwCOevUew/видео.html
What's the piano piece?
yay for exponent math rules...
thought it was ln(x)
It’s log base 2 of x
WHAT IS THE MUSIG IN THE BACKGROUND PLEASE TELL ME THIS IS DIRE
gnossienne 1
@@santiagovalbuenaguzman4459 ILY
What is that weird hook at bottom left
lts just ln(c)=ln(a) + ln(b)
where c=ab
how is log2 particularly useful? you forgot to mention that part
x→log2(x)
which softwares do you use to make these videos sir?
Didn't expect to hear the instrumental extract of the song "Guala" by G-Eazy.
It's classical music. The piano piece is by Erik Satie, not G-Eazy lmao. Look up Gnossienne: No. 1
Just try to listen to the initial few seconds of the short video and then listen to Guala by G-Eazy and Gordo. You will most definitely find it exactly the same.
It may also be the case that they took it from the piano piece that you had mentioned in the reply.
Thanks though.
@@DTLRR it is the case. It's called using a sample, artists do it all the time. Just because he used it in a song it doesn't mean G-Eazy wrote Gnossienne No. 1
@@TheobaldTheBird Yes that I know of. And I did say that he might have used the sample from the original score. And the reason for my uncertainty was - I was ignorant.
Therefore I apologise.
Bro, ln is more important than base 2 log
Y=ax
1+2=3
a+2a=3a
And undeniably this function is even more useful then logarithm😂
Can someone name the piano piece on the backgtound?
gnossienne 1
its just a logarithmetic curve
Log to the base 2
Product rule>quotien rule 🤫🧏🏽♂️
You can't just stop in Middle!
dude.... mindf**k
does this work for numbers that arent powers of 2?
yes just change the base of of the log
@@rusluck6620but would it work when y isnt an integer?
@@braydenshemtov1292 should work i think
Thats the Logarithm of 2
Yine kurtlar vadisi irak mi izliyorsun?
Sliderule
2^1*2^2=2^3
Nice video but logarithmic and analogous curves are not the most useful
Mention tropical geometry without saying tropical geometry…
Oh, OK. A logarithmic curve is the inverse of an exponential. I would have said an exponential. But, it is basically the same.
So this is y=log2(x)
Cool curve
what is that song?
Gymnopedies by Erik Satie
@@barspinoza Wrong, it's Gnossienne no 1.
@@john_titor1 Right. Thanks for the correction.
Yes, it's Gnossienne No. 1 by Erik Satie, composed in 1890. So beautiful.
Please don't torture us with music.
Log curves
Homomorphism
Gotta disagree. Straight lines have had a lot more use since the beginning of mankind.
It s useful but it s far from the most useful
Pls stop making videos with obvious school knowledge and call it “The most … in mathematics”
why is this in my feed. im fucking stupid. don't even know like math past adding
what in the actual fuck are you talking about
Lost me at valid sum
i am on youtube