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The Strange Numbers That Birthed Modern Algebra

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Tom Johnson

The Strange Numbers That Birthed Modern Algebra

The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.

https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/?fbclid=IwAR32bY8dnkg_hCYImiFlJgJL3g_r1CR9Eos4V_YEPcb7bvYJWlTe-8-83fY

TJ

============================================
Tom Johnson - [hidden email]
Institute for Analytic Journalism -- Santa Fe, NM USA
505.577.6482(c) 505.473.9646(h)
NM Foundation for Open Government
Check out It's The People's Data

============================================

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Edward Angel

Re: The Strange Numbers That Birthed Modern Algebra

I wrote the following for Reuben Hersh’s memorial. The story is from when Reuben, Vera and I were in the same carpool to UNM.

During one of our commutes, Reuben and I were sharing the back seat and Reuben brought up the subject of quaternions. For the mathematician quaternions, which are the extension of simple complex numbers from two to three dimensions, have a long and interesting history. Their discovery took a long time even though some of the best mathematicians worked the problem. Nevertheless, they are both simple and elegant. Reuben, of course, loved them for both the history and the mathematics and was going to talk about them in his upcoming class. I mentioned that quaternions are used extensively in computer graphics (any student who takes a class in computer graphics knows about them), animation (for designing camera paths), aerospace (for head mounted displays) and by NASA (in rocket control systems). Reuben was amazed. His response was “Someone actually uses them!?” When we got to Albuquerque, Reuben, still in a state of amazement, dragged me to his class, put me in front, and his introduction was “this guy is going to tell you how people actually use quaternions.” He then sat in the back, thoroughly enjoying my impromptu lecture.

_______________________

Ed Angel

Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)
Professor Emeritus of Computer Science, University of New Mexico

1017 Sierra Pinon

Santa Fe, NM 87501
505-984-0136 (home) [hidden email]

505-453-4944 (cell) http://www.cs.unm.edu/~angel

On Sep 7, 2020, at 2:17 PM, Tom Johnson <[hidden email]> wrote:

The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.

https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/?fbclid=IwAR32bY8dnkg_hCYImiFlJgJL3g_r1CR9Eos4V_YEPcb7bvYJWlTe-8-83fY

TJ

============================================
Tom Johnson - [hidden email]
Institute for Analytic Journalism   --     Santa Fe, NM USA
505.577.6482(c)               505.473.9646(h)
NM Foundation for Open Government
Check out It's The People's Data
============================================
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Tom Johnson

Re: The Strange Numbers That Birthed Modern Algebra

Lovely.

============================================

On Mon, Sep 7, 2020 at 2:27 PM Edward Angel <[hidden email]> wrote:

I wrote the following for Reuben Hersh’s memorial. The story is from when Reuben, Vera and I were in the same carpool to UNM.

During one of our commutes, Reuben and I were sharing the back seat and Reuben brought up the subject of quaternions. For the mathematician quaternions, which are the extension of simple complex numbers from two to three dimensions, have a long and interesting history. Their discovery took a long time even though some of the best mathematicians worked the problem. Nevertheless, they are both simple and elegant. Reuben, of course, loved them for both the history and the mathematics and was going to talk about them in his upcoming class. I mentioned that quaternions are used extensively in computer graphics (any student who takes a class in computer graphics knows about them), animation (for designing camera paths), aerospace (for head mounted displays) and by NASA (in rocket control systems). Reuben was amazed. His response was “Someone actually uses them!?” When we got to Albuquerque, Reuben, still in a state of amazement, dragged me to his class, put me in front, and his introduction was “this guy is going to tell you how people actually use quaternions.” He then sat in the back, thoroughly enjoying my impromptu lecture.

Ed

_______________________

Ed Angel

Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)
Professor Emeritus of Computer Science, University of New Mexico

1017 Sierra Pinon
Santa Fe, NM 87501
505-984-0136 (home) [hidden email]
505-453-4944 (cell) http://www.cs.unm.edu/~angel

On Sep 7, 2020, at 2:17 PM, Tom Johnson <[hidden email]> wrote:

The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.

https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/?fbclid=IwAR32bY8dnkg_hCYImiFlJgJL3g_r1CR9Eos4V_YEPcb7bvYJWlTe-8-83fY

TJ

============================================
Tom Johnson - [hidden email]
Institute for Analytic Journalism   --     Santa Fe, NM USA
505.577.6482(c)               505.473.9646(h)
NM Foundation for Open Government
Check out It's The People's Data
============================================
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FRIAM Applied Complexity Group listserv
Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam
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Steve Smith

Re: The Strange Numbers That Birthed Modern Algebra

In reply to this post by Tom Johnson

Tom -

Great find! I'd never seen the "belt trick" animated like this...

SimTable's progress finally has demanded widespread adoption of quaternions for the "traditional" reason of gimbal lock but with other side-benefits here and there. This has lead to a strong spate of most of the team trying to "wrap their heads around" this abstraction which reminded me that MY head has never fully wrapped itself into the implied Minkowski space, even if I feel like I've "tumbled" through 4D and higher (ala conversations with Dave West on such phantasms) in my VR and Lucid Dream experiences... I can't say I was truly experiencing a complex vector space.

Hise's ( the animator/illustrator in your link) other animations are also helpful:

Gimbal - https://www.youtube.com/watch?v=fRvuIuSkL6Y

I don't believe the connection is anything more than superficial but I, like many here have spent a lifetime fighting tangled power cords, hoses, bungees, and ropes, and watching things tangle, and then untangle this way is pretty familiar/inspirational! I was surprised to discover that the Dirac Belt Trick is homomorphic to professor Caractacus Potts' plate prestidigitatoin.

https://www.youtube.com/watch?v=Qc9h6FC6QgU

(odd factiod, did anyone know that Chitty Chitty Bang Bang started life as an Ian Fleming children's book with none other than Roald Dahl providing much of the movie-versions set and object design?)

ramble,

- Steve

The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.

https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/?fbclid=IwAR32bY8dnkg_hCYImiFlJgJL3g_r1CR9Eos4V_YEPcb7bvYJWlTe-8-83fY

TJ

============================================
Tom Johnson - [hidden email]
Institute for Analytic Journalism   --     Santa Fe, NM USA
505.577.6482(c)               505.473.9646(h)
NM Foundation for Open Government
Check out It's The People's Data

============================================
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FRIAM Applied Complexity Group listserv
Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
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gepr

Re: The Strange Numbers That Birthed Modern Algebra

This book has been in my wishlist for-fscking-ever (https://en.wiktionary.org/wiki/tmesis#English - thanks Dave!):

New Foundations for Classical Mechanics
https://bookshop.org/books/new-foundations-for-classical-mechanics-9789027725264/9789027725264

On 9/7/20 2:48 PM, Steve Smith wrote:

> Tom -
>
> Great find!   I'd never seen the "belt trick" animated like this...
>
> SimTable's progress finally has demanded widespread adoption of quaternions for the "traditional" reason of gimbal lock but with other side-benefits here and there.    This has lead to a strong spate of most of the team trying to "wrap their heads around" this abstraction which reminded me that MY head has never fully wrapped itself into the implied Minkowski space, even if I feel like I've "tumbled" through 4D and higher (ala conversations with Dave West on such phantasms) in my VR and Lucid Dream experiences... I can't say I was truly experiencing a complex vector space.
>
> Hise's ( the animator/illustrator in your link) other animations are also helpful:
>
> Gimbal - https://www.youtube.com/watch?v=fRvuIuSkL6Y
>
> I don't believe the connection is anything more than superficial but I, like many here have spent a lifetime fighting tangled power cords, hoses, bungees, and ropes, and watching things tangle, and then untangle this way is pretty familiar/inspirational!   I was surprised to discover that the Dirac Belt Trick is homomorphic to professor Caractacus Potts' plate prestidigitatoin.
>
>     https://www.youtube.com/watch?v=Qc9h6FC6QgU
>
> (odd factiod, did anyone know that Chitty Chitty Bang Bang started life as an Ian Fleming children's book with none other than Roald Dahl providing much of the movie-versions set and object design?)
>
> ramble,
>
> - Steve
>
>> The 19th-century discovery of numbers called “quaternions” gave mathematicians a way to describe rotations in space, forever changing physics and math.
>>
>> https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/?fbclid=IwAR32bY8dnkg_hCYImiFlJgJL3g_r1CR9Eos4V_YEPcb7bvYJWlTe-8-83fY
>>
>> TJ

--
↙↙↙ uǝlƃ

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uǝʃƃ ⊥ glen

jon zingale

Re: The Strange Numbers That Birthed Modern Algebra

In reply to this post by Edward Angel

Such a wonderful and uniquely Reuben thing to do. I loved to see his delight
in humanity and mathematics.

--
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Barry MacKichan

Re: The Strange Numbers That Birthed Modern Algebra

In reply to this post by Steve Smith

This is not particularly surprising. The two were friends in Washington during World War II, both as British agents. See https://www.amazon.com/Irregulars-Roald-British-Wartime-Washington/dp/0743294580. It is a pretty good book as I recall.

—Barry

On 7 Sep 2020, at 17:48, Steve Smith wrote:

(odd factiod, did anyone know that Chitty Chitty Bang Bang started life as an Ian Fleming children's book with none other than Roald Dahl providing much of the movie-versions set and object design?)

ramble,

\- Steve