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

In the world of mathematics, where numbers are tangible and real concepts, how do you respond to the unknown? Imaginary numbers are used to define something that otherwise is undefined. In this TED talk, Professor Jeff O'Connell, explains to us why imaginary numbers aren't imaginary, and why it redefines our understanding of mathematics and life. Professor Jeff O’Connell is a proud community college graduate with an AA degree from Diablo Valley College. He has his Bachelors in Applied Math from UC Davis and a Masters in Math from San Jose State University. He started teaching in the Ohlone College Math Department in 1995. In addition to teaching classes, Jeff has given several speaker series talks, including Math is Beautiful, the Golden Ratio, Card Counting, as well as Math in the Movies and on T.V. He is one of the teachers in the Ohlone Math Gateway Program which helps STEM majors accelerate math courses while fulfilling other requirements. This past summer, he completed an Ignited Summer Fellowship in the Dynamic Design Lab at Stanford University where they study the design and control of motion, especially as it relates to vehicle safety.

[pocojoyo]

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

[sachinnaidoo]

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

[uwelinzbauer]

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

[rehakmate]

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

[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.

[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.

[Professor_O]

Hi everyone! I'm the speaker from this TED Talk. I've created a series of videos to dive deeper into the concepts I discussed here. If you're curious to learn more, you can start your journey at my YouTube Channel with the video "About my TED Talk." Enjoy! 🤓

[Vonwra]

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

[peta]

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.

[oversquare]

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.

[MrFanBoyDee]

i wish i could like this more than once

[braydencoversbeatles]

This should've went on for another 20 minutes

[laquan]

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.

[homayonreah]

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

[davidroux]

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

[homayonreah]

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

[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.

[bhaskarvk]

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

[StevenSiew]

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)

[ellmango]

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