The Rise and Fall of Quaternions: Why We Use i, j, and k in Vector Calculus | Deep Dive Maths

Discover the fascinating history behind the Cartesian unit vectors i, j, and k, and their connection to the world of quaternions! Join Prof. Jeff Chasnov as he takes you on a journey through the history of mathematics, revealing how quaternions spurred the development of vector calculus. Don't miss this captivating story that combines math, history, and the intense vector algebra wars of the late 1800s resulting in the banishment of quaternions from physics!
00:10 Part 1: Introduction
01:07 Part 2: Real and Complex Numbers
04:36 Part 3: Quaternions
13:26 Part 4: The Vector Algebra War
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[@hohinng8644]

We love you Jeff! Make some more videos/ lectures on various mathematics topic! You are the best online Math lecturer I have ever seen!

[@ProfJeffreyChasnov]

Thank you!

[@lingarajpatnaik3870]

Professor! This is perhaps the best exposition of quaternions I ever came across. May many more people revel in mathematics and learn from teachers like you.

[@gabrielcazaubieilh4342]

This was so instructive and interesting! Thank you Jeff!!!

[@BalrogIsCool]

Amazing video I learned a lot! Really liked the historical parts and I didn't know how strongly connected Quaternions were to vector calculus before watching

[@gh0stable]

Thanks Prof. Chasnov! As a physics student who is also into computer graphics, I find this video to be very informative!

[@ElboxD]

Great video. Thanks!

[@ahmedmuhammed6905]

Thank a lot for such beautiful video

[@musawwirahmad6396]

I was hoping if you could explain what Hamilton meant by the square point and how the allure thereof led him to make his subsequent assumptions.

[@suleimanbas]

brilliant explanation. thank you.

[@segads]

Hey there! Thanks for the video!

[@shayan3354]

Thankyou sir for this insight on this topic .... Really learnt something new today 🙏

[@falvarezarzate1]

Amazing Professor, I also thought, when you talk about the cyclical and anticyclical multiplication, in the Levi Civita symbole that you taught us in your vector calculus course. Thanks for this material. See you soon with much more content too learn from you.

[@mustafaalneami5193]

Thank you professor for this amazing video

[@qhwho7410]

Respect history, put knowledge into proper perspective and context, a great deeds!

[@marioabrantes4932]

Very good!

[@guidopaoluzicusani2185]

I had a superficial knowledge of quaternions but didn't know about the vectors war... nice video! Now cross product and vector product make more sense, too! 😀

[@igormarkov6254]

Thanks!

[@johnzander9990]

Very interesting. Please, more math history.

[@NaseerAhmad-dd6pp]

Thank U sir for mix up maths with real life example by animation interesting vision

[@loading...2876]

Legend!

[@geertdejonge4194]

Thanks, great

[@adeirman7368]

Professor, i think you should add statistics part on Mathematics for Engineers Specialization. Because statistics is super important part of engineering. Thank you Prof.

[@ramazanmert7686]

Perfect

[@EtherealFlowerette]

I love your videos, I wanna a teacher like you. Could you tell your journey of maths?

[@amrabdellatif9956]

I love math history!

[@TV-ll3kh]

I am a physics major and I was completely unaware of this history. That you for teaching me!

[@ProfJeffreyChasnov]

Most people are unaware. Quaternions have really been buried in physics and math.

[@Nickle314]

Would be interesting to do a video on why the cross product doesn't work in more than 3 dimensions. Which leaves onto Geometric Algebra. Interesting that there were attacks on Grassman. I didn't know that.

[@wadesammohamed]

Okay this make sense now

[@amrabdellatif9956]

Hey Jeff! Cool video! I found out about it through your email. Keep sending me emails if they're gonna include videos like these!

[@douglaswolfen7820]

Great video! I found the title a little misleading though. I associate vector calculus with the gradient operator, and div and curl and so on. I was looking forward to seeing how quaternions work when using those operations. But the explanation seems to stop before it reaches the "calculus" part of vector calculus

[@angeldude101]

From what I can tell, the problem seems to be that physicists were trying to use quaternions as points, when they're most definitely not points. The computer graphics crowd actually had the right idea in using them for rotations, because they _are_ rotations. If you're not trying to rotate things, then quaternions would just get in the way. That said, a lot of modern physics, especially quantum mechanics _is_ just rotating things, which is why the physicists have since independently rediscovered quaternions and called them "spinors," which is a much more descriptive name for them, though the notation they use is even _more_ obfuscated than the already obfuscated quaternions.

[@joshuazeidner8419]

oy vey

[@godfreypigott]

"Maths" .... Wow, the correct word! I take it you're not American.

[@ProfJeffreyChasnov]

Haha! I am but I am fond of the s

[@godfreypigott]

@@ProfJeffreyChasnov Good to know. But, sorry, I feel the need to check other Americanisms: (1) Do you pronounce the c in Arctic? (2) Does "buoy" have one syllable or two? (3) [my biggest bugbear] Do you say "I could care less" or "I couldn't care less"?

[@Nickle314]

@@godfreypigottWrite me. One of the Americanisms I hate. The other is burglarized. Take a verb, turn into into a noun, then add an extension to make it back into a verb. Why not just use the verb?

[@godfreypigott]

​@@Nickle314 I can only think of "coronate" at the moment. What other examples do you have? I also hate extro, "gas" for petrol, takeout, "period" instead of full stop, cookies, "in the hospital" instead of "in hospital", "herb" without pronouncing the 'h', pronouncing "semi-" as "sem-eye", drapes, faucet, normalcy, sidewalk, "meet" instead of "meeting", and having no clue what a fortnight is. And one for any fellow mathematicians - saying "quantity squared" instead of "all squared".

[@Nickle314]

@@godfreypigott Out of your list, normalcy I agree. I also hate the rocket launches with 'nominal' instead of normal. On the write me, I suspect that was English when people left England for the US. Then in the 19th century the academics got to work and decided there has to be a preposition. Gas, short for gasoline, I don't object too. herb with no h is odd too. Another perhaps is Cilantro.

[@samholt9177]

Does this guy actually know what’s he’s talking about or is he just reading a script😂😂😂😂😂

[@ProfJeffreyChasnov]

I wrote the script. What's your point?

[@snehangshuroy]

Thanks!