Quaternions are Amazing and so is William Rowan Hamilton!

[@sebastian-azcarate]

I really think math/physics should be teached with history alongside. So much can be appreciated this way! Thanks Kathy for these videos and your book.

[@DJF1947]

Perhaps they should teach English as well.

[@emjizone]

Good teachers put their students in the situation of the previous discoverers, so they don't only deliver the results but also the *joy* of the discovery with the results.

[@larrywildman4381]

Too often schools teach you things like they had fallen from they sky, without the understanding of why scientists got there and how. It's a pity.

[@bradhayes8294]

This is an incredible video! As a mechanical engineer, I've always believed the most enjoyable and intellectually fulfilling way of teaching and learning any mathematically based subject is to include both the mathematics and the history.

[@exsollertan7366]

I very much agree. Sometimes the best way to absorb new concepts is to learn how mathematicians and physicists developed their ideas and how they overcame the pitfalls on the way. John Fannon

[@enricolucarelli816]

I love physics, mathematics, its history... I am 64, and yet, when I listen to your wonderful videos, I feel like a little kid listening mesmerized to the most beautiful fairy tales. Thank you very much ❤

[@Kathy_Loves_Physics]

Aw that was lovely, thank you.

[@pikiwiki]

but are they fairy tales, or, reality?

[@TheMindfulCraftsman]

Great video! As some commenters have already mentioned....Geometric Algebra / Clifford Algebra is the *actual* powerhouse that gives rise to complex numbers and quaternions naturally. As W. K. Clifford's life ended too soon, his work remained almost unrecognized for a long time. Luckily, it was rediscovered and built upon in recent times by David Hestenes. GA has been a real eye opener for me and others. Maybe it will have the same effect on you and inspire you for a new video!

[@korolev23]

If you like quaternions you’re going to love geometric (Clifford) algebra, which finally situates the quaternion concept in its rightful setting.

[@davidhand9721]

Bingo. Complex, Quaternion, and Octonions are all hacks in comparison. Heck, most linear algebra feels like a hack once you know GA.

[@PanglossDr]

Hamilton was an ancestor of mine. When the plaque to him was unveiled at Broom Bridge my Dad was there as one of his closest living relations. I think the genes are still there in the family, I never had any problems with maths and my daughter got a two Es offer to Cambridge at the age of 16 on the strength of her maths.

[@JohnVKaravitis]

What are "E"s?

[@Kathy_Loves_Physics]

They stand for excellent it’s equivalent to an A.

[@PanglossDr]

@@Kathy_Loves_Physics Not exactly. An E is a very low grade, A, B, C, D, E, just above an F for Fail. What a 2 Es offer means is they don't care what grades you get, you are in.

[@PhilFogle]

@@PanglossDr Congratulations on your talented Daughter! May the light of mathematics glow brightly for her...hmmm this is probably historic? Oh well, congrats anyway :))

​@@PanglossDr this, but to clarify it's something that's given to someone who in practice wouldn't have problems at getting to the university/college. It's a "we know you're skilled enough to join, no need to stress on finals" kind of a thing.

[@djredrover]

I am literally using Quaternions for my hovercraft UAV project. I use Quaternions to obtain my vehicle's attitude (roll, pitch, yaw which are Euler angles phrasing but used in Aerospace) to avoid the Gimbal Lock that is inherent in regular Euler Angles method of obtaining attitude from the Inertial Measurement Unit (IMU). In fact, all smartphones also use Quaternions to obtain phone attitude and pose.

[@mekkler]

Quaternions are everywhere. They are used millions of times a second in any modern video game.

[@djredrover]

@@mekkler facts!

[@djredrover]

Also, I am an Electrical/computer Engineer from UBC Canada, and we did NOT learn quaternions in school. Not even the concept. I had to teach this to my self thanks to 3b1b and others.

[@labibbidabibbadum]

Well, then you're obviously a drunkard.

[@TheEvertw]

Not to mention that there are many different variants of Euler angles, all incompatible. Roll-Pitch-Yaw is a different system of coordinates than Pitch-Roll-Yaw, for instance. To make testing nicer, the differences between them are only visible in compound angles, with multiple non-zero values, and are small for small values.

[@keybawd4023]

Your videos are one of the jewels of the internet. As the man, who you may remember spent an afternoon alone in a railway carriage with Otto Frisch, I have to tell you that although -'a long, long time ago' I did-postgrad research on free radicals, your videos make me realize how little I appreciated the background to so many things that, by the time I got to University, I took for granted. Your videos give depth to our understanding of whatever subject you choose. Thank you.

[@Cmurphize]

Dropping out of school for physics 11 years ago left a void. One that you're helping fill. I'm so grateful for your channel. Would have never guessed my interest in history would get me back into physics.

[@jasonzavaglia]

Best teaching on quarternions I’ve ever watched. I never really got it previously.

[@AlabasterClay]

Wow---this is an amazing story. Love, love, love, love it. The history, the biography, the math, they physics. Thank you!

[@Kathy_Loves_Physics]

Glad you enjoyed it!

[@kevinmorgan2317]

Great video. Thanks. Quaternions find their home in 3D computer graphics. Matrices allow rotations about an axis only sequentially and do not work smoothly. Quaternions allow for rotations around more than one axis simultaneously. And they do this faster and use less memory.

[@elderbob100]

I wish I had Kathy as a teacher when I was in school. Kathy loves Physics and it shows. History is actually interesting once you get past dates, names, places and all the other trivia the our educational system fills our heads with. Kathy makes me curious about Physics. She makes me want dig deeper and learn more. Awesome channel Kathy!

[@alwaysfourfun1671]

So delightfull to hear this story. So well told, by a natural teacher. History, as part of Physics classes, could certainly inspire many students, who otherwise would tend to think of the mathematics as difficult and boring. What a wonderful achievement of mr. Hamilton and what an appreciation from the brightest of his time. Deserves to be commemorated with solid teaching in quaternions.

[@HoraceMash]

Wow! This is a tour de force! Thank you so much for opening my mind to the meaning and evolution of quaternions in relation to vector calculus, and the human dimension of these concepts. What a treat to see such a lucid and thoughtful presentation. You are a brilliant historian and science communicator 🎉

[@Kathy_Loves_Physics]

I’m so glad you liked it David. ❤️

[@tomkerruish2982]

They should make a Broadway musical about this guy!

[@Kathy_Loves_Physics]

I would watch TF out of that 🤣

[@leyasep5919]

@@Kathy_Loves_Physics only watch ? not script ?...

[@frankrizzo7454]

Only if they morph him into a black transvestite.

[@b43xoit]

LOL

[@le-m0nke]

@@frankrizzo7454 LOL

[@clay.tennis]

I love the historical perspective, the life you breathe into these amazing scientific pursuits are beautifully woven in with brilliance, mathematics, and nothing left to want for.

[@SciHeartJourney]

Thank you Kathy. I learned about Quaternions doing video game development. They make the math of "rotation" in matrices a bit easier to calculate.

[@pauljmey]

This actually a good jumping off point for the story of Clifford (building on Hamilton) and modern attempts to revive Clifford Algebras for physics (Geometric Algebra, Spacetime Algebra)

[@ProfessorBeautiful]

Thank you,, this is a wonderful thing to rehabilitate the reputation of the Hamilton family, and the quaternions! This was a treat. And, to reiterate, the Lightning Tamers is a tremendous book, a great achievement.... and FUN!

[@Kathy_Loves_Physics]

Thank you so much! ❤️

[@7sArts]

@@Kathy_Loves_Physics Thanks Kathy, excellent look at Hamilton and the importance of quaternions. Not only did you show how they were important to physics, but also to Maxwell and electro magnetism. I firmly believe that Tesla used the time that he spent ill and bed ridden to master quaternions and later used them in his research and experiments to achieve the success no one has yet understood or matched.

[@tomrobla8981]

I worked on missile guidance systems in the 1970s. We used quaternions with Binary Angular Measurement (BAM) to manipulate angles. Real time control calculations using fixed point arithmetic.

[@mcello47]

Brilliant! As much as I admire all of Hamilton, Maxwell and Gibbs, I wasn't aware of the common historic thread that united them. Thanks for such an inspiring piece!!

[@susilgunaratne4267]

Thank you very much for giving us the clear picture of vector calculus & its discovery.

[@nnfefe9451]

Hello Ms., you too are a mathematician because you able to explain effortlessly what other mathematicians had written. Thanks.

[@TexRenner]

I do watch for the history, but you make the math interesting enough I would not want to skip. Nice of you to offer.

[@rgoodwinau]

Wow! Inspired youtube recommendation of an inspiring youtuber! Thanks Kathy.

[@Arfonfree]

Years ago I studied fluid dynamics and fell in love with vector mathematics. However, I never followed the history any further back than Edwin Bidwell Wilson. Thank you so much for this video. It has opened a new window for me into this fascinating world.

[@briannewman9285]

I'd *love* to have this lady as a math prof.. She is enchanting.

[@NEMOPMORPHY]

So glad I found your channel, this is amazing!

[@Cherokee140Pilot]

Kathy, After you passed basic Algebra, you lost me. And yet, I found myself enthralled by your storytelling and enthusiasm for Mr. Hamilton. Great video, and you have a new subscriber! 😊

[@ErikHare]

Two biographies. One for a quaternions and one for Hamilton. Sounds great!

[@shawgeasland2096]

Wow!!!! Another high quality channel to nerd out over!!!! I am so excited!!!❤🎉

[@robertschlesinger1342]

Excellent video. Very interesting, informative and worthwhile video. BTW, Euler, a German surname, is pronounced as one might pronounce "oiler," rather than the Americanized pronunciation sounding more like "youler." Your many videos are very interesting, worthwhile, and a great benefit to many people wanting to broaden their horizons into the physical sciences.

[@robbannstrom]

Oh, this is great - thank you Kathy for this video. I remember meeting a member of the physics faculty when studying astrophysics years ago, and he was "well-known" in the department for studying quantum mechanics using quaternions - I never did find out what they were until now! Also, as a radio ham, I look forward to your series on the evolution of wireless - it's sure to be really interesting...

[@BruceCurrell]

Your enthusiasm is adorable. [And contagious]. Thanks for all the hard hard work you do.

[@jdp9994]

Beautifully done! It would be wonderful if this continuing tale is tied in with Clifford Algebra/Geometric Algebra, which I think gives further weight to Hamilton's intuition of the important role these can have in understanding "the mathematics of the physical universe".

[@AxisAngles]

Fantastic video. Thank you so much, I never knew how fundamental quaternions were to so much modern mathematics.

[@spaceranger3728]

When I was in grad school taking classical mechanics, quaternions were mentioned briefly but we never got into them. But then when I found myself out working on space shuttle simulators, it suddenly became evident how much more efficient it was to describe rotations with 4 quaternion elements instead of direction cosine matrices. In those days, computing power was limited and passing rotations from one processor to another took a lot of number crunching.

[@DFPercush]

Why 4 quaternions? Isn't one sufficient to express the orientation of the craft? Or are those others for things like gyros?

[@drtidrow]

@@DFPercush He's referring to the four elements of a quaternion, versus the nine in a matrix. There's a lot fewer floating-point operations using quaternions than using direction cosine matrices.

[@DFPercush]

@@drtidrow Oh, of course, derp. :P

[@hp127]

I simply love your way of enlightening about the history and mathematics. Thanks

[@lourias]

I really did not grasp all of calculus until I encountered Calculus in the 3 dimensions. Then, boom, I have been "hooked" since. It is beautiful that crochet is calculus wrapped in knots 🪢, stitched knots🪢.

[@jamesbond_007]

Outstanding! Incredibly enlightening -- loved the associated historical narrative of Hamilton's life! Well done Kathy!!!

[@Kathy_Loves_Physics]

Thank you so much!

[@hereigoagain5050]

Thanks Kathy for sharing the human & social side of math and physics. Math is the greatest, continuous creative effort of civilization. It is easy to forget that there was a time when it did not exist.

[@jameszmuda6362]

Absolutely right. The whole mystery of the meaning of the dot product and vector product is made clear once you see both of them just “pop out” of the operation of multiplying out two quaternions. I always wondered where those (seemingly arbitrary) definitions of vector products came from.

[@zackstaboy]

Wonderful video. As a supplement, it is fair to say that Clifford/Geometric Algebras are a definitive extrapolation of the true promise of Quaternions (along with the Cayley-Dixon algebra sequence). Either one of two particular 7:04 Clifford Algebras provide a beautiful environment for framing relativistic physics - as emphasized and developed by Hestenes.

[@multiplysixbynine]

I love it! As you described how quaternions informed vector analysis, my mind was abuzz with new connections tying back to some math and geometry I have been working on lately while writing software. Like most folks, I learned vectors well before quaternions and some of their connections may have been obscured to me by familiarity.

[@jacejunk]

Spectacular! I always enjoyed the story of Hamilton's discovery of quaternions (and appreciate their modern application in computer graphics), but did not realize how integral they were in inspiring vector calculus.

[@X-boomer]

Excellent work Kathy. I’ve always found this stuff impenetrable until now.

[@zetristan4525]

This is so awesome of you! Kathy, you're a force of inspiration

[@mortenwesteraa7910]

Extremely good video. Thanks so much Kathy, for sharing this and correcting history. You make the world a better place.

[@Cor97]

Thank you for this compelling presentation of a remarkable person.

[@petsatcom]

Another fantastic and interesting scientific mathematical video.

[@nativesun7661]

You’re doing such a fantastic job!!!! Thank you. Great channel for both history and math!!👏🏾👏🏾

[@dominiquefortin5345]

It was very interesting to see how the development of quaternions lead to matrixes, vectors and geometric algebra. Today, you can simplify Maxell equations in terms of geometric algebra.

[@DougMayhew-ds3ug]

Fabulous tour of Hamilton, I love the warmth you bring to this sometimes cold world of mathematics and physics; it’s contagious. Just a beautiful and outstanding approach! You truly bring these people and ideas back to life, and make the subject approachable for the curious but intimidated crowd.

[@matthewhunt6525]

Kathy your awesome I freaking love your mind and your work

[@h2energynow]

Always a deeper insight into some amazing people who influenced our lives. Thanks for this incredible video.

[@joehelm5072]

BRAVO! A great job realigning facts and history, connecting the dots on the arrow of math and its applications!

[@GiI11]

Kathy, I absolutely love your videos. I watched this as a break from studying for my QM final and was shocked to notice that the couplet notation is alive and well in the mathematical treatment of Hermitian products. It's somewhat ironic that we now regard Hamilton's greatest legacy as his development of Hamiltonian mechanics while most physics undergrads will never see quaternions in a lecture. Fortunately, their very notion hangs out in the back as something interesting to learn about. It blew my mind to learn that the i,j,k unit vectors we use in additive vector notation evolved from Hamilton's analysis of i,j, and k as the negative roots of unity. Very very cool. You certainly deserve all the success you get

[@Kathy_Loves_Physics]

Good luck on the final. You’ve got this 👍

[@tddybr78]

Awesome, as usual! People should learn more about quaternions as undergrads. Not to mention Hamilton. Best, Ted

[@TheAlison1456]

you wrote a book, that's awesome! great video, what a great biography.

[@tubbyoneness]

I love your channel. This is my absolute favorite episode so far. Bless you for the work that you are doing. You have combined this fascinating information with your incredible and contagious enthusiasm to make something that is truly wonderful.

[@Kathy_Loves_Physics]

Wow, thank you!

[@otiebrown9999]

Kathy, I am an EE. Only casually did I hear anything about this math genius. Heavyside, greatly helped with Maxwell's Equations! Thanks!

[@MrAaronvee]

Heaviside[sic] was insane.

[@joystickmusic]

Thank you for setting the record straight again! I've watched all your videos and I learn a lot. When I was a kid, my father always used to explain physics and math through te personal quests these researchers and mathematicians were on, so these videos hit close to home, in a good way. (I think you can just leave the bloopers out. They do not add to your stories.)

[@craigslist6988]

what an amazing history exploring video with such dense information presented but with such a smooth flow, thank you.

[@MartinLopez-mo7tm]

Wonderful video. Hamilton is renown for the Hamiltonian of quantum mechanics, honor enough. A video on the Hamiltonian and the Lagrangian would certainly be welcome. I understand it's a tough one.

[@verticalit8]

For another take on the "Victorian Brain War" (fictional?, or factional-to-death?) between Vectorists and Quaternions, see Thomas Pynchon's Against the Day. Thanks to Kathy for another inspiring history lesson!

[@edwardhaglin2322]

That is why I thought this would be fun .I loved that book .as a big Gravity's Rainbow fan .and Pynchon admirer.

[@tedsheridan8725]

What an utterly fascinating video! As someone who's pretty familiar with quaternions (I took a picture with the Broome Bridge plaque during my trip to Ireland last month), I was only vaguely familiar with the history of vector calc., let alone Hamilton himself. I was taught that quaternions were replaced by vectors, and I only actually learned them much later. You do a fantastic job of showing how quaternions were the OG's of it all. Can't wait to see more on your channel!

[@sennest]

I'm out of my water here, a simple shop teacher who teaches the practical maths and sciences who absolutely loves your work. There's something compelling in what you do and how you do it!😎👍👍 Please don't stop🙏🙏 because of your histories I try to inspire my students. Maybe one day...

[@nathanwestfall6950]

Another great video! Thank you for your dedication, research and hard work!

[@treborg777]

This was wonderful, thank you for doing this video. I had been confused about quaternions for some time, and this helped me immensely.

[@Kathy_Loves_Physics]

I’m so glad

[@drtidrow]

Indeed, I had thought that vector calculus had been developed independently, instead of evolving directly from quaternion math.

[@djredrover]

7:32 I believe the correct pronunciation is "Oil-er". (I used to say "you-ler" before too until my Russian friend corrected me, although the pronunciation is more French-sounding).

[@TheBrainn]

William Hamilton is my favorite mathematician of all time. Basically invented vector calculus and revolutionized linear algebra. Makes me proud to be irish too.

[@BarriosGroupie]

I'm so glad you mentioned how he introduced complex numbers as ordered pairs of real numbers which I find to be more profound than his invention of quaternions. I think his need to interpret quaternions geometrically lead him astray from their original algebraic simplicity.

[@pauleohl]

I was wondering why I never heard of quaternions until you got to the part about dot product, cross product, divergence and curl, all of which I did learn as an undergraduate Mechanical Engineer: Pratt Institute 1965.

[@leehaelters6182]

Yay for Pratt, I loved that steam powerplant that lit the whole campus!

[@pauleohl]

@@leehaelters6182 As i recall, the steam power plant made DC only which was used for lighting and the elevator in the building which powered the steam plant. The spent steam was piped to radiators in that same building for heat in the winter. The whole building burned down in 2013. The floors were soaked with oil from the lubricators on the reciprocating steam engines. When did you graduate? What was your field?

[@jbsmathers]

Don't ever stop making these videos or writing your books! History will find such work more valuable than the incomprehensible theoretical gibberish dominating physics today.

[@lylecosmopolite]

A physicist who shares your derogatory opinion of fundamental physics in recent decades, is Sabine Hossenfelder, who KZbin channel has been a very active one for 10+ years.

[@pikiwiki]

Don't ever stop! Ever!

[@londonmackerel7462]

I love this video and, even though I have a maths background, learned a whole lot of new stuff. It is great to find someone who also loves the history of mathematics and physics. Your enthusiasm is infectious and inspiring. You do a fab job.

[@Kathy_Loves_Physics]

Glad you enjoyed it!

[@Roommate625]

This content should be on PBS to expose a larger audience to your amazing teachings. Your enthusiasm for the material and delivery remind me of the TV show Connections.

[@Kathy_Loves_Physics]

Thanks. I’m game if PBS is.

[@lawrencedoliveiro9104]

Not sure if you knew this, Kathy, but _Connections_ was a documentary series on the history of science and technology hosted by James Burke. The first lot of episodes was from 1978. There were two more called _Connections II_ and _Connections III_ , as well as _The Day The Universe Changed_ . The key motif was the progress does not proceed in straight lines, but lurches in all kinds of different and unexpected directions. All still well worth watching.

[@therealpbristow]

​@@lawrencedoliveiro9104 I loved that series! James Burke was another fabulous explainer, coming to the world of science and technology via a humanities background. One of several guys deliberately recruited by the BBC to present and "translate" anything that might be too technical for audiences, when they were covering things like the Apollo Space program (which he famously did alongside Patrick Moore).

[@jeffm3865]

This was pretty fantastic. I appreciate your research and delivery to educate others. I was searching to see if you had any videos on Fourier, but I didn’t see any. I haven’t found much on Fourier’s origins and early work that eventually led to Fourier series and Fourier analysis. I believe he was once in Napoleons army in Egypt and based some of his early work on maximum rate of firing cannons so they will not melt. Unfortunately, I haven’t been able to find many sources so I’m not sure if the cannot firing source was true.

[@marc-andredesrosiers523]

I learned so much! Thanks!

[@AT-27182]

Hamilton was incredible and your telling of his story is exciting and helpful. Thank you so much.

[@Kathy_Loves_Physics]

So glad you enjoyed it.

[@NormReitzel]

This was great. Loved the math! Much better than Kaplan's "Adsvanced Calculus" - and putting it in terms of quaternions makes it intuitive! (IK, so I'm a little weird). Still, I appreciate your very educational video. 👍🖖

[@ffggddss]

Marvelous treatment of the development of vector calculus from "hypercomplex number" algebra! I especially picked up on Hamilton's observation relating to the sum of squares of the components. In my undergrad years as a math major, one of the most singularly stunning theorems I recall, was one which stated that if an algebra of n-tuples is to be formed with a norm equal to the sum of squares of the components, in which the norm of a product equals the product of norms,* then n must be 1, 2, 4, or 8. Period!! This excludes all but real numbers, complex numbers, "hypercomplex numbers" (quaternions), and octonions. * In which the components of the product are bilinear in the components of the factors. Fred

[@xyz.ijk.]

One of your best videos! This was outstanding. Thank you so much for this work, and for clearing up the misapprehensions about his life.

[@vaibhavtheinventor5437]

Amazing video I've learnt a lot

[@banlbsc]

Some great mathematics emanating from Ireland in that era, Boole (at Cork), Hamilton and also George Stokes who had a hand in vector calculus.

[@TielhardSJ]

You missed the Parsons family and the Leviathan.

[@elizabethfrootloop7814]

When I was in 12th grade I enrolled in vector calculus at Yale, the highly theoretical version of the course for math majors. They never told us about j Willard Gibbs or the influence he had on what we were learning. The next year I attended Yale and The chemistry professor couldn't stop talking about Gibbs however, and how he is buried on campus. Eventually I got a PhD (not at Yale) but only recently discovered I am a direct academic descendant of Jacobi of the Jacobean. Than you for your rich history tying my academic identity and work into the full fabric of the human experience.

[@alexkalish8288]

Very well done and complete. Very creative mix of the math and history. Quaternions are not taught anymore - just studied by math history aficionados.

[@kennethcrandall8131]

Another great video! Consider taking a short course in German. My hero Leonhard Euler would appreciate it! In fact, I would love to see you do a history of Euler and his tremendous mathematical contributions.

[@TheEvertw]

Seconded

[@jceepf]

I use quaternions in my work all the time!!!! I am an accelerator physicist. The spin of a particle rotates around in an accelerator. You can represent the rotation using quaternions (same as spin in Quantum Mechanics). The resulting map, around the machine, has an invariant called the "n"-vector or invariant spin field. In the linear regime, very close to the central orbit of an accelerator, the quaternion representation of this rotation gives us immediately the invariant direction. In the nonlinear case, it is not immediately obvious but the quaternion greatly eases the computation of this spin field.

[@jpgsawyer]

Excellent stuff. As a Mechanical Engineer too I use Quaterions quite a lot. They are the best way to use rotations. :D Yeah for rehabilitating historical figures who get raw deals. :(

[@tomstrum6259]

Never heard of "Quaternions"...This absolutely the most Incredible unbelievable story I've ever heard...That any 1 person could accomplish 1/10 of this is unbelievable....This is certainly a distinct higher evolved human species !!

[@EngineerNick]

That was an amazing story thankyou :) I always assumed the dot and cross product were invented first. I guess the dot and cross product are just so much more intuitive having easy to remember rules and properties. But when it comes to interpolating between orientations in 3d space, quaternions are still king.

[@juhakivekas2175]

Thank you William Rowan Hamilton, Carl Friedrich Gauss and Willard Gibbs. You made life quite a bit easier for many of us. Of course there are many more that owe so much. Science is a cumulative treasure.

[@yusong1141]

I can't believe my luck when I found thus video. So so so goog! I enjoy every single minute of it.

[@osmanfb1]

At 24:44 I saw names of Clifford (Clifford algebras), and Grassmann on Gibbs' paper. So, Gibbs was aware of the connections between them way back then. Nowdays Geometric Algebra.

[@recklessroges]

Hamilton is one of my heroes. Thank you for doing him justice.

[@Kathy_Loves_Physics]

I’m so glad that you feel like I did him justice

[@niconeuman]

Excellent video! As always! Now I understand quaternions much better, thanks!

[@John-pp2jr]

7:33 Euler is pronounced OILER. Fantastic video❤️

[@Tobascodagama]

My professors were all quite insistent on this as well!

[@Kathy_Loves_Physics]

Wish mine were - would have saved me embarrassment today.

[@amazing7633]

@@Kathy_Loves_Physics This is a standard difficulty for geeks in physics and mathematics who know words only from reading them. Our physics department had two professors who had worked on the Manhattan project and thus had little difficulty attracting guest speakers who were well known in nuclear physics. One of the students pronounced "new-kyew-lar" when speaking to a famous guest and got a withering correction, "Nu-cle-ar, please!"

[@nicholaslederer]

@@Kathy_Loves_Physics I think we all came here to learn and can appreciate the learning process. Keep making awesome videos (and mistakes to learn from)!

[@ThisHandleIsTakenChooseAnother]

What a great video. The Hamiltonian in popular science doesn’t do justice to how much this legend contributed to matrix operations and understanding of imaginary numbers and how they relate to geometry.

[@leyasep5919]

Another awesome video with a fascinating story !

[@Kathy_Loves_Physics]

Glad you enjoyed it

[@leyasep5919]

@@Kathy_Loves_Physics Like ALL your previous videos. You are so fabulous ! Please keep going !