How I Feel About Logarithms 

I agree. I need to use it in a book somewhere.

new favorite quote

-Vi Hart 2013

Yes, that got caught in my cool-trap, too! Reminded me of an early SNL routine, I believe it was Christopher Guest and Gilda Radner: GR: That's so cruel! CG: Well, Gilda, sometimes you *have* to be cruel. GR: To be kind? CG: No, to be *even crueler!*

Why does the copied comment have more likes? Look at the comment below people!

Same.

-Sarah- this is gold

and thats just at the half way

-Sarah- pls

oopsie... ha! no, not noticed but you are right :O

NO WAY i actually didn't and that's extra funny now lol

that just has sense in english and not in every english spoken place

@@Xayuap most puns are unique to a language, thats just how it is

@@an3_omx not just to a language, they're even unique to a defined culture, place or niche

+Vihart You should write a book!

+WeAreTheInsurgents she exceeds that. She is a mathmatical Goethe.

***** You do ;-)

+AWWSHEET Grossly underestimating her fanbase, bro.

+lowiigibros I went to Goethehaus once. I am quite fond of the few weeks I spent in Germany. I like to think her fanbase is one of the more cultured ones.

I'm using this to teach my pre-calc class :D

You don't listen/think do you?

Guy That what were YOU thinking when you wrote this? Honestly, just wondering

@@arqamislam3877 probably that the stuff she's talking about is simple if you just listen or that she doesn't really talk about it properly or she's confusing But I don't remember this video

@@guythat779 I think vi appeals to a specific type of person. For me, I enjoy mathematical truth more than most other things, but I'm also tragically intellectually lazy. Vi's very good at giving you just the right framing of logic to allow a glimpse at the simple majesty of mathematical truth, without having to do the hard work required to gain a real, deep, intuitive understanding of it.

Matt McIrvin same here haha

+Matt McIrvin just some temporal corrections.. I am going to quote that. "Sometimes to make the harder things simple, first you have to make the simple things harder." There that is better.

But how that's any good? It's "you'll get it when you'll know all basics", which is rather trivial and obvious.

​@@KrzysiuNet To me it means that the simplest way to explain a thing is not always the most general or extensible way to explain it. Sometimes you have to go back and reformulate the simple things in a form that seems unnecessarily elaborate, so you can extend it into a new realm.

OK, thanks! Now I got what you mean :)

haha you sound like such a creep

Learner-Learns "beautiful hands"...?

Christian Faux :P

Christian Faux :P

Very charming, isn't it? She's like a mermaid singing math melodies.

And I am amazed that it is called "natural". Well, as you can tell, I'm not very good at math.

Mathematicians are not known for giving things good names

Why, engineers? :p

The Jacman : as as i know, it stands for logarithmus naturalis.

Lorenz Mayer Thus the "ln" acronym. I guess base e is really something to warp ones head around. Is there a number system in base e? I do some research on this.

Essentially, yes, she has. Which is why the alternate name for this video is "On the Nature of Mathematics as a Whole by Victoria 'Vi' Hart"

lerch25 this is so beautiful

Logarithms are elementary algebra skills. This is a topic you won't even see in an undergraduate class let alone a master's thesis... I've got news if you think this is remotely tough. lol

Eric You could extend an explanation of addition all the way to real analysis, and I guess you COULD still call it 1st grade math.

The world of mathematics is becoming daunting for people and I don't understand why. I suppose its the failure of the common core method. Students these days just are not nearly as able. Regardless if it is elementary level or not.

+ethan z To be honest: Sometimes they also multiply by 1 or add 0. The fundamental part of mathematics is expressing two or more things differently until you see that they are the same.

Elchi King I like where you're going with that, but can you simplify the last part a little bit?

ethan z Hm, I don't know if I can simplify the last part, but I could try looking for examples to explain it. Since I want to find good examples, it may take me some time.

ethan z OK, I think, I've found some examples: Let's start easy: We can look at the number "2" as the smallest even number or as the smallest prime number, which will give us different point of views on the (same) number "2". We can also look at the number "1" as the/a generator of the whole numbers when it comes to addition or look at it as the neutral element when it comes to multiplication. Speaking of numbers, we can define prime numbers as natural numbers greater than 1, which are only divisible by 1 and themselves, or we can define them as the natural numbers n, s.t. Z/nZ is a field, or we could define them as generators of maximal ideals of Z... each of these views will give different aspects of prime numbers. And we can even get a little bit more complicated: If we look at reals numbers, we could define them in the way of there "invention", i.e. we start with natural numbers, go to whole numbers, find fractions i.e. rational numbers and then "fill in the gaps" (i.e. we add all limits), or we could define them (i.e. the real numbers) using axioms and define "the" rational numbers as the minimal subfield of this field (up to isomorphism). If we go these ways, we can see, how real numbers can be constructed out of whole/rational numbers but we also see, why we can say that rational numbers "are" indeed a part of the real numbers. Let's move on to geometry: We could look at "the" unit circle as the set of all points which have distance 1 to the point (0,0). This is of course possible. But if we want to calculate intersections, surface areas etc. it might be useful to look at the plane as the field of complex numbers and identify the circle with the set {exp(it)| t real}, thus giving our problems an "algebraic" touch which might be easier to solve. Speaking of planes, let's go to incidence geometry (i.e. we only care about intersections of lines/Objects): When we draw pictures of landscapes there seems to be an "infinitely far away" point at which parallel lines intersect. Guess what: We can describe this "infinitely far away" properly and get projective geometries. In more detail [the following paragraphs might be hard to understand since I'm only presenting results without explaining much]: the "intersection properties" of a "plane" as we usually know it can be described as an affine plane: 1) For any two different points there is exactly one line, which connects them. 2) Given a line l and a point p. Then there is exactly one line, which crosses p and does not cross l unless it is already l. (i.e. for every line l and every point p there is a parallel line to l through p) 3) There are at least three (or four) points, which are not all on the same line. if we want to include "infinitely far away" points, we get this (a projective plane): 1) For any two different points there is exactly one line, which connects them. 2) For any two different lines there is exactly one point, which both cross. 3) there is a quadriliteral (i.e. four points of which no three are on one line) From these axioms we can at some point deduce, that every projective plane can be turned into an affine plane by removing one line and all of its points (i.e. "dropping out infinity") and every affine plane can be turned into an projective plane by "adding infinity" and, that these processes are eliminating each other (up to isomorphism). So we can conclude, that the painted picture we see is actually "the same" as the "real" world, only in a projective way. And when it comes to projective planes we get two nice examples: First: Look at the surface of a sphere. If we look at the intersection of two great circles we will see, that they always intersect in two points which are "poles" (i.e. they are exactly on opposite sides of the sphere). If we identify these two points with each other, we will indeed get a projective plane. Second: Look at the 3D-space. If we look at planes as "lines" (I will call them "newline") and lines as "points" ("newpoints"), then newpoints and newlines form a projective plane if we say that a newpoint is on a newline iff the corresponding line is part of the corresponding plane. But then we look again at these two examples and "see" (of course it is a bit difficult as I didn't explain much) that these two examples are actually the same (when it comes to their structure as projective planes). And then there is the role of Desargues' and Pappos' theorem, which are some statements about properties of projective spaces/planes. As it turns out, Desargues' theorem applies if and only if there is a vector space such that the affine plane corresponding to the projective space "is" (isomorphic to) this vector space, and Pappos' theorem applies if and only if the field which is defined by the vector space is commutative. (i.e. we can (in a way) describe algebraic objects geometrically and vice versa) One last example (actually, this is also some kind of projective geometry): When we look at complex numbers and holomorphic functions we can get to a point at which it is usefull to identify infinity with one point and thereby making the complex (with added infinity) plane (isomorphic to) a surface of a sphere. By using Moebius transformations we can now rotate this sphere and thus make "infinity" to a finite point... And at the same time we get, that lines and circles are actually the same things: Lines are circles with an infinite diameter. Or: Lines and circles are actually projections of great circles of a sphere on the plane: If we use stereographic projection, the northpole will get "infinity", great circles running through the northpole will become lines and all the other great circles will become circles... I hope, you can understand at least one or two of the examples :) Feel free two ask (but I don't know, if I can explain it in a simple way)

Hope you enjoyed writing that as much as I did reading it, sounds good, peace!

Dat Epic Fish That pun though!

she is!!!! look how many people learned/relearned what logs are and now can see how they work and even possibly smell them, she taught us all a little bit of that

School teachers don't get much freedom in the curriculum. Making youtube videos is much more effective in that sense.

Winter Summers This was not algebra.

Does everyone have to be a stickler for everything? Do you not realize that this is the basis for algebra?

elleveldy Algebra is just arithmetic. If this isn't algebra, then what is?

Peter Thomas Jesus, just google algebra ffs

Okay. "Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process." This video is talking about the patterns of arithmetic, algebra (at least the regular kind familiar to any high school student) is literally just an application and shortcut of these EXACT same patterns. It's not something else, it's just a short hand way of dealing with things like "3 times a distance plus 5 times the same distance, is just 8 times the distance." You don't even have to know what the distance is because it works for ALL of them, because Algebra is just shorthand of arithmetic with unknown values (at least as taught in high school).

Everything changed when the fire nation attacked

Aye but zero just tells all the +1s what they are tho

That still traumatises me. ..

That's when I reduced it to half speed and watched 3 more times (in a +onesey sort of way). But, is there a way to watch the explanation in a timesy s.o.w.? I have some real catching up to do.

She taught you not learned you...

ScouseGaming Teach?

A13Xplicit Yes the teacher taught her/him and they learned off the teacher

Gold Stars for everyone!!!

unfortunately there's no nobel prize for math :l

*64

64

@fernando657 Oh so bored today

And she's amazing at it. :D

Wait till you see the rest of the videos then, it'll be your dream come true.

I need more thumbs!!! I'm actually starting to get this now. So why did a need a 92 euro calculator to not get it.

Please do not. Most of the Khan videos are painfully slow when you grew up with this style of narration. Sal means well, but I wish all the time he'd say things once and get on with it.

Aanzeijar I get your point, but please be advised that these videos are 'painfully slow' WHEN you grew up with them. Most of us didn't. And the EUR92 calculator is compulsory for the upper two levels in Dutch high school (which takes about 25-35 percent of pupils). And that's bloody steep for still not getting it, if I'm honest.

ThePietjoo Hahahaha LOL. Your absolutely right. I should have gotten this 10 years ago. But I'm not top 35%. Had to buy it for a bachelor build environment (hbo Bouwkunde). I just wan't to see it, to get it. And not get taught how to put it in your calculator.

IMHO, HBO Bouwkunde qualifies for upper '35 percent' of pupils as you need HAVO/VWO/MBO+ level to enrol. Remember, I'm talking CITO-score here and therefore 25-35% of the entire population, instead of 25-35% of HAVO/VWO. But now, all I really want to do is find the thing an play bomberman. ;)

I've always intuitively thought about numbers in similar ways to in this video. At least for addition, subtraction, multiplication and division.

Matthew Mitchell those four are the boring ones. i even got thought in school that you can think about multiplication just the way she discribed it. the fun part is where Vi gets to roots and logs.

Are you telling me that every time you see 5x8 you count by 8's five times or by 5's eight times? Doesn't seem incredibly efficient.

Mike Ehrmantraut Well after doing multiplication for so many years, you do eventually come to memorize them. But when you are learning you should have an idea of what you're actually doing. That way you'll never be confused about why 5x8=40 when you know that you can just count by 8s to verify.

Your teacher sucks lol... Perhaps the easiest way -- really second easiest way -- to _do_ multiplication is through memorization, but memorizing is not learning. I really hate when people memorize a lot of what they're to be learning instead of actually learning it, but that's their own mistake, which is the best kind of mistake.

Your teacher wasn't wrong; she just wasn't very good at expressing herself. The easiest way to *use* multiplications is just to memorize them. The easiest way to *understand* multiplications is to think of it as repeated addition. It's left as an exercise for the Philosopher to decide which of those activities best describes "learning."

Both are important. If you don't understand what multiplication is, you are going to have tremendous trouble with mathematics going forward. Everything will seem like a completely arbitrary black box to you, and therefore will be entirely meaningless and very difficult to remember. You will also be very confused by word problems and any kind of application. However, it is definitely worthwhile to also memorize one's times tables. I'm a straight-A math student and have always preferred understanding and recreating formulas/facts to memorizing, but there is a role for memorizing. That role is automaticity. There's only so much room in one's working memory at any given time. If you just know your multiplication facts, this frees you to think about something bigger. This knowledge is almost useless without a deeper framework of understanding, yes, but it is definitely helpful! An analogy: I used to play the piano, but even after years of practice I was terrible at reading music. I had only memorized a handful of treble clef notes. Even so, I could sight-read music by figuring out the correct note to start with and then looking at intervals. So if I start at C, and then the next note is one whole step lower, I play a B next, and so on. Being so attuned to intervals was useful to me, but it was also problematic in that it enabled me to get away with not memorizing which note was what, and ultimately made sight-reading much harder for me.

Yeah most math communicators do have a fair amount of formal math education, and then they put their own spin on it. So im sure she's aware

'Simplified'? Such as leaving out all that arrant nonsense about the 'smell' of numbers?

SpectatorAlius Maybe that, but breaking out the parts about negative integers for later, and powers/roots.

SpectatorAlius What about another way of looking at it: smell is just fancy counting! Break your VOCs into hydrocarbon chains, break them into compounds and elements, and then count protons and electrons. The transfer of electrons between the VOCs and your smell receptors sends an electric signal to your brain which just counts them up and tells you what you smell! Or something like that.

Why? How does your education system work?!? In my education system, you get this obvious and natural explanation in elementary school, and it's the only possible explanation, in my opinion. WTF is wrong with your education system?

aa Murica! Actually, it's most schools. A public school I went to was great.

Why don't you change it.

potato 123 I did recently, forgot to update the comment. It used to be "illdiewithoutpi" but now it's "illdiewithouttau". Doesn't rhyme anymore, but I can justify it better.

but hey tau rhymes with you, right?

No.

illdiewithoutpi I still see pi there!

***** Nah she just gets high of the sharpies (just kidding)

***** Nah it's probably a smell fetish.

+TheiLame I also kind of get the "2 and 4 and 3 in a cubic-y way" feel when I think about 8 lol.

-ignore this please-

+TheiLame I wondered that. Could be!

oplz oplz Derivatives and Integrals, gah! I can do them perfectly on paper, but I just can't fully understand them as the concepts that they are!

You can try looking up the website khanacademy! I really recommend it :)

The only things you'll ever need to know about sin and cos (that can be used to jog your brain about every other property of sin and cos) 1: upload.wikimedia.org/wikipedia/commons/0/08/Sine_curve_drawing_animation.gif If you go around the perimeter of a circle and trace your x co-ordinate over time or your y co-ordinate over time, you create a sine wave. Sine waves and circles are two sides of the same coin. Furthermore - if you imagine a right angled triangle as having one point in the center of the circle and the hypotenuse being the radius of the circle, you can use this fact to jog your memory about which ratios of sides give you which trigonometric function, etc! 2: If you draw a sine wave, then draw a second wave on the same chart that, at each point, goes higher if the sine wave is currently ascending, 0 if the sine wave is currently flat and goes lower if the sine wave is currently descending, you get... a cosine wave! That is, the cosine wave is the derivative/differential of the sine wave, and therefore the integral of the cosine wave is the sine wave. (-sin and -cos fill the gap if you keep differentiating/integrating.) 3: For bonus points, learn the Taylor Series for sin and cos and why they are that way: www.khanacademy.org/math/calculus/sequences_series_approx_calc/maclaurin_taylor/v/maclauren-and-taylor-series-intuition

Clearly, you need to stop and smell the factors.

or clearly WE CAN START MATHS ALL OVER AGAIN xDD or not o_o...

listen again it's worth it

Ikr, then you get to high school, and they're like "Forget that boring stuff, now is time for you to discover"

AnonymousDuckLover You end up with a whole generation of secondary students who hate math because they struggle to understand and keep up, which has two major long-term impacts: 1) The people who go into professions that require math don't know how to do it; and 2) We get fewer people going into math education and fewer teachers who understand math, further perpetuating the vicious cycle.

If, when you watch Vihart's videos, you feel this kind of indignation towards teachers, you've completely missed her message. It's the individual who internalizes mathematics. No teacher can convince you theorems are true. You must convince yourself that it's true (or argue why it's false). Ask yourself: How does Vihart relate math concepts to the real world? Then ask: How can I relate math concepts to the real world? Vihart had to have asked those questions. She did her work to find the solutions. This is her presentation. Where's yours?

MasterThief1324 I don't feel indignation towards teachers, I never said that. I feel frustration towards a system where teachers teach an area they aren't comfortable teaching; particularly one with such dependence on early understanding. This isn't always nor entirely their fault, so it doesn't make sense to blame teachers specifically. Next, I find it absurd that you seem to think the teacher's contribution is some binary does/doesn't; that because it's the individual that must understand, the teacher somehow takes no blame for a student's poor understanding. Of course not; that's what teachers are for, improving the students' understanding. A teacher poorly-versed in math teaching it themselves is a recipe for students who can't do math. This is bad. Me? I would not be a good teacher and I accept that. Instead I put my actual skills to use by writing and drawing up examples and worksheets for an after-school remedial math program for elementary and middle school students. _This is my current job._ So now what? If you feel the need to demand my personal contribution to math education just because I'm criticizing the _actual_ current status of math education that has _real_ consequences, how about you? If you assume I'm not doing anything to help the situation and want to criticize me for it, then surely you yourself must have some ground to stand on. Otherwise you're just saying that I shouldn't criticize because I'm not helping, and that would be silly!

you just my every thing that ill need in life in to 9 min and to that i give you a : )

Tyler Chandler I wish every single elementary, middle and high school teacher saw this video, changed how they taught math and then students would have more time to do more interesting things! If someone asked my advice I'd say, "Learn EVERY SHORTCUT you can" and that "YES, the teachers ARE trying to trick you - you're not imagining it." Thanks Tyler, your comment made my day!

: o yyyyaaaaaaaaaa

You might want to check out Knuth's up-arrow notation: en.wikipedia.org/wiki/Up_arrow_notation

Hyperoperations and the successor function. You're welcome.

I believe the latter is far more likely.

Nicholas Hernandez Either way, cheaper in the long run. :D

CTVadim So would that be -1, -1, -1 kids?

Math, man. Math.

Hey, I'm 23 and I don't even know what Logarithm is.

By super exponentials, I assume you mean tetration (iterated exponentiation: "power towers"), pentation, and other hyperoperations? I've always been surprised that tetration doesn't play a larger role in mathematics, but I suppose every level below it (addition multiplication, exponentiation) shows up far more often.

energysage I think the reason why tetration doesn't show up as much is because it's not continuous - no one can agree on the best, most exact way to extend tetration to real numbered heights. Perhaps there is a way, perhaps there isn't.

energysage The reason tetration doesn't show up is that numbers get really big really fast under that operation. Exponentiation is just slow enough to show up in scientific and engineering applications, while tetration is way to fast to be useful to almost anyone. The only people I could see using them would be physicists, as they often deal with huge numbers (combinatorics of the universe) or possibly number theorists (for incredibly large prime numbers, for instance), but these cases are so sporadic that it's not worth it to make others learn the notation.

energysage indeed I do. Those operations have various names.

Really? Because I'd think that even a child could understand this.

As the lady said, "to make the hard things easy, sometimes you have to make the easy things hard."

Jordan Shank I am a child I understand kind of

Mind if I join you?

Nah, be my guest. Misery loves company.

This isn't the best introductory video to logs. Go and learn about logs from a textbook or teacher etc, and then you'll be able to appreciate the video :)

Olii Sant I learned it from Khan Academy. www.khanacademy.org/math/algebra/logarithms-tutorial

2+3 is 2 add one 3 times. 2*3 is 2 times itself,2, 3 times. Both of the inverses of these functions are simple as 2+3 = 3+2 and 2*3 = 3*2, so for instance it doesn't matter if you ask "What times 3 is equal to 6?" or "What do you times 3 by to equal 6?" because however you define division you will get 6/3 = 2. Now instead of adding itself 3 times we now look at 2^3 which multiplies 2 by itself 3 times, which is 8, so it makes sense for the inverse to ask "What to the power of 3 equals 8?" which is ³√8. But what if we want to know what 3 is to the power of to equal to 8? If you use the same inverse function we have ³√8 = 2 but 3^2 = 9, not 8, so instead we have logs as a second inverse function and say log(3) 9 = 2 which asks "What to you put 3 to the power of to equal 9?"

+princeofexcess Vsauce did an awesome video about that

+Daniel Corkhill link

+Luna Don't be lazy - You have the name, you have the topic, the world is yours. Go now