Imaginary Numbers Are Not Imaginary | Jeff O'Connell | TEDxOhloneCollege

[@kb9043]

Imaginary numbers might sound like math's version of make-believe, but this talk really shows how they're the bridge to solving things we thought were impossible. Jeff O'Connell nails it, math isn’t just numbers, it’s a whole new way of seeing the world. 🔥

[@pocojoyo]

He didnt make the connection between the imaginary numbers and the oscillatory motion he described at the beginning.

[@_ArtofLife]

I was thinking the exact same thing...

[@collegemathematics6698]

Its not a math lecture to prove the application of complex numbers in mechanics, this topic is already known for centuries i gues. He just mention that imaginary numbers are not imaginary based on how we benefet from them in real life.

[@sachinnaidoo1559]

Man's secretly a hypnotist making the audience imagine the imaginary numbers

[@rehakmate]

Is it just me or did this video not explain anything, like what was the point of this?

[@chronicsnail6675]

TedTalks...

[@pocojoyo]

You are completely right. He didnt make the connection between the imaginary numbers and the oscillatory motion he described at the beginning.

[@pocojoyo]

@Samson Jamari you dont have a girlfriend, incel

[@rehakmate]

@Samson Jamari lol

[@mingledspringle]

@Samson Jamari das crazy yo but who asked

[@uwelinzbauer3973]

Brilliant and convincing introduction to this interesting topic - to be continued on and on. Certainly he is able to share the enthusiasm with the audience

[@ellmango]

the presenter started with very easy to grok examples, and then introduced the "we need to know square root of -1" as though the beginning examples showed that, without illustrating why that would be in any way.

[@Player-pj9kt]

You have to learn about differential equations to understand why

[@eyobwalid2332]

Bold of you to assume enough people know about differential equations for that to be a reasonable statement

[@carultch]

@@eyobwalid2332 I don't think Player was assuming that the audience knows differential equations. Just that in order to give a proper introduction to show why these examples have anything to do with sqrt(-1), would require an introduction to differential equations that would significantly make the lecture longer and probably lose half the audience.

[@carultch]

If you are wondering the reason why his examples have anything to do with sqrt(-1), here's why. A differential equation that models vibrations, like the mass on a spring, is given by: m*y" + k*y = 0 where m is the mass, and k is the spring stiffness. y is the position of the spring at any point in time t. y" refers to 2nd derivative of y, which in this case is acceleration. One of the strategies for solving a DiffEQ in this form, is to assume y = e^(r*t), where e is a constant called Euler's number, and r is an unknown constant we'll solve for. Applying this to the DiffEQ, we end up with: (m*r^2 + k) * e^(r*t) = 0 e^(r*t) cannot be zero, so instead we solve the polynomial in front of it for r, to make that polynomial zero. Had the sign in front of k been negative, we'd have real solutions for r, equal to +/-sqrt(k/m). The solution then, would be a linear combination of exponential functions. However, the solutions are imaginary, and r = +/-sqrt(k/m)*i. Assign w to equal sqrt(k/m), to simplify our writing. This means the general solution is a linear combination of both of them. Assign arbitrary constants C1 & C2, to form this linear combination: y = C1*e^(i*w*t) + C2*e^(-i*w*t) Let C1 = (A + B*i)/2, and let C2 = (A - B*i)/2, where A and B are another two arbitrary constants. Our goal is to cancel the imaginary parts we'll eventually produce, so we can find a real world solution for y. y = (A + B*i)/2*e^(i*w*t) + (A - B*i)/2*e^(-i*w*t) Expand out e^(i*w*t) and e^(-i*w*t) with Euler's formula: e^(i*w*t) = cos(w*t) + i*sin(w*t) e^(-i*w*t) = cos(w*t) - i*sin(w*t) y = (A + B*i)/2*[cos(w*t) + i*sin(w*t)] + (A - B*i)/2*[cos(w*t) - i*sin(w*t)] After expanding it, you'll eventually cancel out all i's. The B/2*i*sin(w*t) terms add up, and so do the A/2*cos(2*t) terms. y = A*cos(w*t) + B*sin(w*t) And just as you expect, an oscillation is described by a linear combination of sine and cosine waves. No i's anywhere in this, which means this all happens in real numbers. But to show it from first principles, we had to appeal to imaginary numbers.

[@Vonwra]

He did not reveal anything extra ordinary. 30 seconds of insight spread over 10 minutes.

[@Player-pj9kt]

This video is meant to be an introduction to complex numbers not an extraordinary revelations. If you want to read something extradition then read a mathematic/ science journal

[@peta1001]

I personally went a long way passing math exams which proved only the fact that I can follow the rules and the routines. However, accepting the "command" that negative numbers exist set me off what seems to be a natural logic or intuition. Why, I thought a lot? When we count pocket coins or "rocks on the beach", we either have them or we do not (the sum is either zero or greater than zero). When we measure something, though, as it may be a distance between two points or our body temperature, we might accept that having a refence point is practical way to express that some things are on the other (opposite) side (like temperatures below freezing point or tuning frequencies of music notes etc.). Yet, even though we accepted that reference points are only practical for labeling scalar values, someone decided to build on the "convenient truth" and stated that "negative number" to the power of two is always a positive number. That definitely excludes the possibility that we use the exponentiation on the other side of the reference points (temperature values below zero raised to the power of two, for instance, give you the same result as the positive numbers...). What scares me the most is...how far in quantum mechanics, which is trying to get ideas from the math (full of "convenient truths"), can we get. Do we really want to believe that one particle can me in two places at the same time? Or...is it a high time we got rid of convenient truths and/or approximations (that some mathematicians questioned through history...) and than tried to understand the quantum mechanics and the string-theory.

[@oversquare6625]

numbers are only tangible through common experience. it is fair to say all numbers are imaginary - they exist only in our shared imagination. complex numbers themselves are little more than an index of rotation - basically the unit circle.

[@keithjohnson3324]

Exactly this!

[@gudnavar]

The title of the talk brought me to click on this video but nothing really revealed. There are another 8 minutes to explain further. There are other videos (example by Welch Labs) that explain the concept in depth.

[@ravi.thaker6039]

Same

[@laquan3661]

Imaginary...aren't negative numbers technically imaginary? If not, physically represent a negative amount of anything as you would show me a positive amount of apples. If physically representable is the standard of real numbers, then the only real numbers are positive numbers. If non-positive numbers can be real, then a number that is non-positive and non-negative can be real also.

[@jmhorange]

Real numbers are one dimensional. Imaginary numbers help make numbers 2 dimensional with special properties around multiplication for the imaginary number, namely i is a 90 degree rotation on a graph that repeats every 4 cycles under exponents. Multiplication of course doesn't work that way with real numbers. The names themselves are not important, it's just positive and negative numbers need to be in the same group of numbers since they share all the same properties and we have chosen to call that group, real numbers. Real numbers, negative numbers, imaginary numbers are technically "real" numbers if any number are real. Imaginary numbers were discovered when trying to solve cubic equations, which involved 3 dimensions and cubes, ie the real world we live in. Unlike quadratic equations where if they encountered square roots of negative numbers, they could decide there was no answer as visually on a graph it means the quadratic equation doesn't touch the x axis to have an real number answers, cubic equations have to cross the x axis at least at one point to give an answer because of their shape. There's some cubic equations with real numbers, that has an answer that's a real number. And for these specific equations, if you use the cubic formula, you must encounter the square roots of negative numbers. These eventually cancel out while doing the math to get the real number as an answer but you have to reckon with how to solve for the square roots of negative numbers to solve the formula. That's the original reason for the number i. With that you can solve for any answer in a cubic or any polynomial of n degrees, it will have n degree solutions. You can go back and solve for the answers of those quadratic equations that didn't seem to visually touch the x axis to have an answer. If they aren't found among the reals, they'll be found in the imaginary plane. All those imaginary answers perhaps don't exist in the real world, but the logic behind those imaginary answers stem from the original solution of specific real world cubic equations that had real numbers, that you had to pass thru the imaginary plane to arrive at the real number answer.

[@homayonreah1955]

What space/ deep meaning imaginary numbers represent(generally)??

[@sepulous]

I was hoping he would use the oscillatory motion to concretely show a situation in which complex numbers are necessary for describing a real world phenomenon. Like MrBeen said, he just didn't make that connection, and that's a bit disappointing.

[@saroshrizvi2498]

Best prof at Ohlone. No 🧢

[@mathijsjacke1915]

Professor​ @user-ky5dy5hl4d

[@homayonreah1955]

How can e^iπ which is a positive number be -1 ?

[@davidroux7987]

One can describe damped oscillations with purely real numbers... e^(-gamma*t) * cos(omega*t +phi)

[@brunoborma]

He didnt explain why 😭

[@braydencoversbeatles4029]

This should've went on for another 20 minutes

[@MrFanBoyDee]

i wish i could like this more than once

[@NoAnimePD]

Best professor!

[@bhaskarvk5558]

I like your lectures sir , I'm from 9th standard😊

[@sciencedoneright]

TOTALLY REMINDS ME OF WELCH LABS

[@Charlie-vj9rf]

You need closed captioning

[@StevenSiew2]

I was taught that e^(i theta) = cis(theta) so e^(i male) is a cis(male) and e^(i female) is a cis(female)

[@carultch]

Completely unrelated meaning of cis. Cis in this context, is a notation for cos(theta) + i*sine(theta). The c from cosine, the i from the imaginary unit, and the s from sine. Cis as in cismale and cisfemale, is the opposite of trans, and is a loanword from chemistry's use of the word. Look up cis and trans isomers, and it will make perfect sense to you, why cismale and cisfemale mean ordinary male and ordinary female.

[@cucumber_999]

yeah I thought so

[@chucksucks8640]

This is just a random mini-proof but if -1 < 0 => sqrt(-1) < sqrt(0) => sqrit(-1) < 0 therefore an imaginary number lies on the real number line. I know this isn't true but I found it intriguing.

[@mahmudurrahman5759]

شكراً

[@jiahajime5815]

Wheres the sub?

[@ellmango]

the presenter didnt fully explain a single line of thinking that wasnt already assumed to be understood by the audience.

[@sirasapbflo510]

Yesterdays appetizer: Casadilla

[@nuranichandra2177]

Too much hoopla, glitz and glammer in the beginning and the clip ends with a whimper

[@dalecollins477]

Another example of a man who has missed the main point of why imaginary numbers are needed in the real number system we have currently. If you choose to call the left of 0 negatives then they don't have the same algebra outcomes as positive numbers; i.e., the square root of a positive number is just a positive number, but the square root of a negative number doesn't exist. In reality, numbers left of 0 are no different to those on the right, because there are no negative numbers in nature.I challenge you to find one! It's only things like accounting where you need to represent debt and hence our ancestors came up with negatives as an axiom on the real plane. If you want, you can call the numbers left of 0 left 1, left 2 left 3 etc and now the square root of say left 4 is just left 2..... no need in that system for imaginary numbers! Euler and all the others either didn't realise this , or chose not to change the axiom of negatives to non negative labelled numbers. If you think about it, using the 'take away' operator (I.e. negative, or -) as a position as well seems to be a bad idea as it is just an operator. Similarly using positives (+) on the right is superfluous as it makes no difference to any positive results and is also just an operator. I suggest to make sense of the universe we need to use a non positive / negative set of numbers. Leave negative / positive systems for accounting. Btw, I understand imaginary numbers are great for all sorts of things in engineering, but they (i) is just a fix for a previous axiom mistake as said above.

[@markelijohnjavierpascual4112]

nice. we need new math about this

[@felipediazcristianismo]

He did NOT explained anything. I just wasted 10 minutes of my attention. THUMBS DOWN.

[@ptptp7826]

Euler's Iden Diddy

[@Thegeometer-ep3sj]

Excellent job!! One of the very best educators at Ohlone!

[@edwinlu123]

He couldn't explain anything. Maybe it's like a cult.

[@Player-pj9kt]

You have to learn about differential equations to understand how it relates to springs and pendulums

[@paigeluben4970]

Totally reminds me of Alton Brown!!

[@muramallagayathri7728]

Who is Alton brown ??

[@pocojoyo]

hahaha me too.

[@chadwarner4245]

That’s what was going through my mind!

[@enochsadventures]

they are imaginary.

[@sambrown9494]

Why do these videos never seem to go anywhere? You had my attention, why just stop? Or was it all about the attention? Not impressed.

[@pulseofages]

You know which number I made up? Klevin. And Gaupp. I feel sad for those who don't understand this 😂

[@MyOneFiftiethOfADollar]

I feel equally sad for your parents and anyone else who has to keep your company for extended periods.

[@godofgodseyes]

Jeff O'connell, Can you show me imaginary number representations with apples, oranges and bananas? Hope you can think simple things deep.

[@robogamer2023]

Yes you can

[@Professor_O]

Haha - I guess I should check the comments more often. Sorry for the late reply! The answer is no! Imaginary and complex numbers will never be the answer to a real life application. They are a tool that allow us to solve real life applications. I hammer is a tool that, all by itself is not that impressive, but what you can do with a hammer...

[@chronicsnail6675]

@@Professor_O bro how is hammer comparable to the imaginary unit smh ur not teaching maths 😂

[@Player-pj9kt]

​@@Professor_Oimaginary numbers are essential for understanding circuits and current flow

[@abhishekgusain1082]

Oiler🤣🤣

[@tugcebetulyakarer8715]

Pendulum is the paid actress

[@luigimelon3334]

pog!

[@dhananjeyannatarajan5366]

wassup

[@YashKakrecha]

27M subscribers and 7k views...

[@savagedeuterium374]

Really a waste, nothing explained.

[@soikatmaji4685]

totally waste of time

[@q.m9094]

This was the absolute worst ted talk. Waste of time.

[@professormawillett4297]

Nah, they’re just a tool to understand the real world.

[@digitalbook8503]

@user-ky5dy5hl4d I think real no. are symbols and along with axioms and operations, we use them solve real physical problems like geometric problems and things which we can touch and feel their existence. But at some point in history when mathemasians tried to solve problems like cubic equations, BTW in past mathematicians justify each step of solution by giving proof using geometrical shapes or other things which we can count or measure like when solving 2+x=6 mathimaticians solve it by imagining that there are 2kg and a weight of X kg on one side of beam balance and 6kg mass on otger side of beam balance so when we do 2+x-2 = 6-2 they justify this by saying that we are removibg 2kg weight on both side as the wieght on one side of balance left is x and other is 4 and it is balaced so it means that X wieghts 4kg so x=4 but at solving cubic equations they came across some steps in solution which have square root of -1, but there is no such thing in the world which can make sense i mean when i say square root of 4 it means 2 so mathematican immediately at that would place 2 apple or 2 meter length depending upon which physical thing they are using to justify each step, but when they started solving for cubic eq they find that square root of -1 occur in the middle step as an intermediate but at the end in the result such numbet cancel out and gave only answer in real no. Only. But they said how can we justify that step having square root of -1 because no such thing exist in nature so they said why not we form a number system which is multiple of square root of -1 though they don't have physical interpertation but they can be used in middle step of solving real world problem so these numbers were invented to help algebric calculations not to count physical thing but when complex plane was formed they thougt that, since square root of -1 make numbers on number line rotate so can be useful to take track of such system which in teal world rotate by asinghing one quatity to real axis and other to imaginary axis but remember imaginary numbers unlike real number are not invented to count physical things but they were invented for algebric world to solve its problems and the answer of real world problems but imaginary part at the end will cancel and answer will be in real numbers always! If real world answer is possible and if it don't come than it means it don't have real world solution!

[@Player-pj9kt]

​@user-ky5dy5hl4dthey are essential for circuit analysis and current flow

[@dasmegacool]

That fools left hand was moving all over the place I saw him dab a few times!!!

[@Professor_O]

I did the best I could 😜

[@High_Priest_Jonko]

Terrible talk

[@MyOneFiftiethOfADollar]

Please share your immense intellect by enumerating your reasons the talk was terrible.

[@dominikbaricak9589]

Waste of time

[@pixelapse9613]

How?