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The rotation problem and Hamilton's discovery of quaternions I | Famous Math Problems 13a
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with his wife. This represented a great breakthrough on an important problem he had been wrestling with: how to algebraically represent rotations of 3 dimensional space using some kind of analog of complex numbers for rotations of the plane.
This is the first of three lectures on this development, and here we set the stage by introducing complex numbers and explaining some of their natural links with rotations of the plane. There is a lot of information in this lecture, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further. In particular the last slide (page 9) could easily be stared at ...
published: 17 May 2013
-
Quaternions are Amazing and so is William Rowan Hamilton!
Quaternions are amazing, they made modern vector mathematics. But how were they created and how do they work? In order to explain all that I am providing both a fun biography of Hamilton AND a biography of quaternions and the couplets that led to them.
My website: http://www.KathyLovesPhysics.com
My book "The Lightning Tamers" on Amazon: https://amzn.to/3I7N4mq
Patreon: https://www.patreon.com/user?u=15291200
AudioBook Go Fund Me: https://www.gofundme.com/f/donate-to-help-me-make-an-audiobook?utm_campaign=p_lico+share-sheet&utm_medium=copy_link&utm_source=customer
Anne van Weerden's Website:
https://annevanweerden.nl/Entrance.html
"A Victorian Marriage"
https://annevanweerden.nl/VictorianMarriage.html#Publications
Full song of "William Rowan Hamilton": https://youtu.be/SZXHoWwB...
published: 31 Jan 2023
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Land Rover Discovery | Project Discovery with Laird Hamilton
Land Rover Ambassador and big-wave surfing pioneer Laird Hamilton is no stranger to displaying resilience in the face of one of nature’s most powerful forces. After a year of unprecedented challenge Laird mirrors Land Rover’s Project Discovery and examines the source of resilience itself. Find out more: https://bit.ly/3D4J56e
published: 02 Oct 2021
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The rotation problem and Hamilton's discovery of quaternions III | Famous Math Problems 13c
This is the third lecture on the problem of how to extend the algebraic structure of the complex numbers to deal with rotations in space, and Hamilton's discovery of quaternions, and here we roll up the sleaves and get to work laying out a concise but logically clear framework for this remarkable structure.
A main tool that we will use is the algebra of 2x2 matrices, however with (rational) complex number entries. This allows us a simplified way of proving the various laws of arithmetic for quaternions, and brings ideas from linear algebra, like the determinant and the trace of a matrix, into play.
We end with an important visual model of quaternions and the key formula that connects them with rotations of three dimensional space. There is a lot in this lecture, so be prepared to go slow...
published: 24 Jul 2013
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The rotation problem and Hamilton's discovery of quaternions (II) | Famous Math Problems 13b
This is the second of three lectures on Hamilton's discovery of quaternions, and here we introduce rotations of three dimensional space and the natural problem of how to describe them effectively and compose them. We discuss the geometry of the sphere, take a detour to talk about composing planar rotations with different centers, talk about the connections between reflections and rotations, and introduce the basic algebraic framework with vectors, the dot product and the cross product. As in the first lecture, there is a lot of information here, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further.
Euler's theorem on the composition of rotations is an important ingredient. You will also learn that a curious addition of spherical vectors ...
published: 01 May 2013
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The rotation problem and Hamilton's discovery of quaternions IV | Famous Math Problems 13d
We show how to practically implement the use of quaternions to describe the algebra of rotations of three dimensional space. The key idea is to use the notion of half-turn [or half-slope--I have changed terminology since this video was made!] instead of angle: this is well suited to connect with the lovely algebraic structure of quaternions.
The theory of half turns is interesting in its own right, and belongs to what we call Vector Trigonometry--an interesting variant of Rational Trigonometry that we intend to describe in detail elsewhere. Here we only need a few formulas for half turns, which really go back to the ancient Greeks and the rational parametrization of the unit circle which we have discussed many times!
By focussing on the formula for quaternion multiplication in terms of s...
published: 09 Aug 2013
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Discovery Conference 2023 Hamilton Morris and Robin Carhart Harris
Discovery Conference is The Bay Area's annual Psychedelics conference at The Midway in San Francisco. Get more information at www.discoverycon-sf.org.
published: 16 May 2023
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Did Hamilton Somerville's Wife Commit His Murder?
Hamilton Summerville dies of a toxic drug overdose. His family believes that his wife, Donna, is motivated by greed and money as she’ll inherit everything.
For more go to http://www.investigationdiscovery.com/tv-shows/vanity-fair-confidential/
Vanity Fair Confidential
MONDAY 9/8C
#VanityFairConfidential
Subscribe to Investigation Discovery | https://www.youtube.com/user/DiscoveryID
http://www.investigationdiscovery.com -
---
True Crime Files by Investigation Discovery
Add Hundreds of Crime Shows to Amazon Prime - Start Your 7-Day Free Trial Today!
http://investigationdiscovery.com/TrueCrimeFiles
published: 25 Mar 2016
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AWURADE YE LIVE By DIANA HAMILTON At Trinity Baptist Church Ghana || PL Crew ||
I want to thank you all for your continuous support. This is only the beginning!!! MUCH LOVE❤️
LIKE, SHARE & SUBSCRIBE to my channel
Let’s become friends
Instagram - https://www.instagram.com/its_nyb/
Facebook - https://web.facebook.com/NyB-927723850688902/
Snapchat - nyb70
#dianahamilton #jesus #music #viral #ghana #drums #youtubeshorts #youtube #party #praise #church #musician #energy #dance #vibes #groove #drumming #subscribe #share #explore #discovery #musiclife #trending #vlog #joemettle #trends #bandlife #world #inspiration #motivation #passion #explorepage #fyp #concerts #band #family #afrobeat #dianahamiltonsongs
published: 25 Feb 2024
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Project Discovery | Laird Hamilton
Big-wave surfing pioneer Laird Hamilton is no stranger to displaying resilience in the face of one of nature’s most powerful forces. After a year of unprecedented challenge Laird examines the source of resilience itself and looks forward to new adventures.
Learn more about the Discovery: https://landroverau.click/discoYT
published: 11 Oct 2021
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23-Year-Old Mystery Solved: The Shocking Discovery of William Dashawn Hamilton's Murder
This video revolves around the 23-year-old mystery of William Dashawn Hamilton's murder, which was recently solved. The video starts by emphasizing the significance of the truth and how it can never be concealed, no matter how long it takes. It further explains how criminals often think they can get away with their crimes, but the truth will eventually catch up with them. The host welcomes the viewers to AF Crime and urges them to like, subscribe, and turn on notifications to stay updated on future uploads.
The video then moves on to the story of a young reporter named Angeline who, in 1999, was called by the police chief of DeKalb County in Georgia to investigate the discovery of a child's remains in a nearby cemetery. Upon reaching the site, Angeline was horrified to find the remains of...
published: 20 Mar 2023
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Kaitlin Hamilton - Discovery Talks
The Ohio State University's Kaitlin Hamilton delivers her Discovery Talk 'Mitochondria and Macrophages: New Directions in Cystic Fibrosis Research.' Presented by Infectious Diseases, a focus area of Ohio State's Discovery Themes.
published: 20 Feb 2018
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The World's Most Potent Psychedelic | HAMILTON'S PHARMACOPEIA
The Bufo Alvarius toad can have its venom glands milked for the powerful psychedelic 5-MeO-DMT. But conservationists have warned that could threaten the survival of the species.
Watch more from VICE TV:
Hamilton Morris Spews After Taking Peyote
https://www.youtube.com/watch?v=nTr3dW0RRlM
How Not to Cook Meth
https://www.youtube.com/watch?v=FtTZ-CZ_a4Q
Using the Psychedelic Iboga to Treat Addiction
https://www.youtube.com/watch?v=YEL71eGc6DQ
#VICETVArchive
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Follow VICE TV:
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Newsletter | http://bit.ly/1kpnyN6
published: 06 Dec 2022
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Bryan University - What is e-Discovery Project Management by William F. Hamilton
published: 23 Mar 2012
-
Amazing Dinosaur Discovery | Hamilton NZ | 2020
Amazing Dinosaur Discovery | Hamilton NZ | 2020
https://youtu.be/6gwqj9wimz4
Subscribe to Our Youtube Channel – JNS Videos
https://www.youtube.com/c/jnsvideos
Like Our Facebook Page
JNS Videos : https://www.facebook.com/videos77777/
Amazing Dinosaur Discovery, JNS Videos, Dinosaur Kids, Dinosaur, Hamilton, New Zealand, Te Rapa, Pukete
#AmazingDinosaurDiscovery #JNSVideos #DinosaurKids #Dinosaur #Hamilton #NewZealand #TeRapa #Pukete
published: 23 Jan 2020
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Land Rover Project Discovery | Laird Hamilton
Surfpionier Laird Hamilton staat er om bekend dat hij is opgewassen tegen de enorme natuurkrachten van de oceaan. Na een jaar van beperkende omstandigheden geeft Laird zijn visie op Land Rover's #ProjectDiscovery en evalueert hij waar het bij menselijke veerkracht om gaat.
Meer Discovery: https://bit.ly/3ahQQti
Beleef Land Rover online:
Website: http://www.landrover.nl
Facebook: https://www.facebook.com/landrover
Twitter: https://twitter.com/landrover
Instagram: https://www.instagram.com/landrover
published: 10 Oct 2021
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Connect to Hamilton - OCE Discovery
We partnered with the entire #HamOnt innovation ecosystem at this year's Ontario Centres of Excellence Discovery event!
Event-goers connected to Hamilton as we brought together McMaster University & Mohawk College, Innovation Factory & The Forge - Hamilton, Hamilton Economic Development, and partners from across this city.
We were joined by innovative Hamilton start ups like Nix Sensor Ltd., Lumago Inc., Brüha, OverAir, Cinnos, 180 Drums, Nuts For Cheese, Aiva Labs and so many more. What an amazing opportunity to connect our city and bring the entire ecosystem together!
Check out the video here:
published: 25 May 2017
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Tripping on the World's Oldest Psychedelic | HAMILTON'S PHARMACOPEIA
In Season 3 of HAMILTON'S PHARMACOPEIA, Hamilton journeys to South America on a quest to understand the legend of Bufotenine – the world's oldest psychedelic.
Watch more like this:
Hamilton Morris Meets Meth Addicts Hooked on God
https://www.youtube.com/watch?v=fJDGJgB_AKI
The Toad Venom Pamphlet That Changed Psychedelia Forever
https://www.youtube.com/watch?v=3WMA1_PdgRQ
Tripping on Hallucinogenic Frogs
https://www.youtube.com/watch?v=C3Yd7M3JNlw
Subscribe Now: https://vice.video/SUBSCRIBE-TO-VICETV
Follow VICE TV:
VICETV.com | https://www.vicetv.com
VICE Video | https://video.vice.com
Facebook | https://www.facebook.com/vicetv
Twitter | https://twitter.com/vicetv
Instagram | http://instagram.com/vicetv
Newsletter | http://bit.ly/1kpnyN6
published: 21 Dec 2021
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The Toad Venom Pamphlet That Changed Psychedelia Forever | HAMILTON'S PHARMACOPEIA
Haunted by his past mistakes, Hamilton embarks on a journey to correct an error in his reporting while identifying the origin of an international toad venom smoking phenomenon.
In Season 3 of HAMILTON'S PHARMACOPEIA, Hamilton continues his odyssey into the historical, chemical and societal impacts of some of the world's most unique drugs. He learns more about LSD, bufotenine, 5-MeO-DMT, DMT and more.
Watch more like this:
The Fish That Gets You High
https://youtu.be/6N3j5g066CU
Hamilton Meets with a Cacti Expert
https://youtu.be/jgADsY_vWkI
Hamilton Morris Meets with Folk Healers of Thailand
https://youtu.be/p-dXRqYU7-Y
Subscribe Now: https://vice.video/SUBSCRIBE-TO-VICETV
Follow VICE TV:
VICETV.com | https://www.vicetv.com
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Facebook | htt...
published: 07 Dec 2021
-
Hamilton County Discovery Workshop Invitation
@jpmcdon John McDonald invites you to be a part of the upcoming Discovery Workshop in Hamilton County.
published: 21 Dec 2023
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(Discovery) From Hamilton Episode 4. Man vs Wild!! 人在第4集
published: 14 Sep 2019
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Digital Discovery Gala 2020 - Hamilton Chapter
ProAction Cops & Kids is building trust and relationships between cops, kids and communities. Prepare to be inspired!
Learn more: https://www.copsandkids.ca/
published: 14 May 2021
-
Delicious Discovery: Shanghai Restaurant SkyCity Hamilton Food Review | First-Timer's Impressions!"
Join me on my Yum Cha journey as I venture into the delightful world of Shanghai Restaurant at SkyCity Hamilton for my very first food review! From mouthwatering dishes to the ambiance, I share my honest thoughts and impressions. If you're a foodie or planning to visit SkyCity Hamilton, this review is a must-watch for a taste of what awaits you at Shanghai Restaurant. Don't forget to like, comment, and subscribe for more exciting food adventures! 🍜🌆 #FoodReview #ShanghaiRestaurant #SkyCityHamilton #FirstTimeEater
published: 09 Dec 2023
58:24
The rotation problem and Hamilton's discovery of quaternions I | Famous Math Problems 13a
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with h...
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with his wife. This represented a great breakthrough on an important problem he had been wrestling with: how to algebraically represent rotations of 3 dimensional space using some kind of analog of complex numbers for rotations of the plane.
This is the first of three lectures on this development, and here we set the stage by introducing complex numbers and explaining some of their natural links with rotations of the plane. There is a lot of information in this lecture, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further. In particular the last slide (page 9) could easily be stared at for an hour or two.
Even old hands at complex analysis may find something novel here to stimulate their thinking, as I insist on a completely logical and rational approach to mathematics--no waffling with angles or ``transcendental notions/functions'' involving ``real numbers''. In fact such a pure algebraic approach is exactly what is needed to set the stage for a good understanding of quaternions.
In particular you will learn that the most fundamental fact about complex numbers is properly stated using the notion of quadrance, that turns are a viable substitute for angles, and that the rational parametrization of a circle is intimately linked to a quadratic map at the level of complex numbers. These ideas will prepare us for appreciating the rotation problem in three dimensions, which we tackle in the next lecture, and then the introduction of quaternions, which we explain in the following one.
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist?
list=PL8403C2F0C89B1333
Year 9 Maths: https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
Ancient Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
Wild West Banking: https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
Sociology and Pure Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: https://www.youtube.com/playlist?list=PL55C7C83781CF4316
Wild Trig: Intro to Rational Trigonometry: https://www.youtube.com/playlist?list=PL3C58498718451C47
MathFoundations: https://www.youtube.com/playlist?list=PL5A714C94D40392AB
Wild Linear Algebra: https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
Famous Math Problems: https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
Probability and Statistics: An Introduction: https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
Boole's Logic and Circuit Analysis: https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
Universal Hyperbolic Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
Differential Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
Algebraic Topology: https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8
Math Seminars: https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
Six: An elementary course in pure mathematics: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
Algebraic Calculus One: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
Algebraic Calculus Two: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
м
https://wn.com/The_Rotation_Problem_And_Hamilton's_Discovery_Of_Quaternions_I_|_Famous_Math_Problems_13A
W. R. Hamilton in 1846 famously carved the basic multiplicative laws of the four dimensional algebra of quaternions onto a bridge in Dublin during a walk with his wife. This represented a great breakthrough on an important problem he had been wrestling with: how to algebraically represent rotations of 3 dimensional space using some kind of analog of complex numbers for rotations of the plane.
This is the first of three lectures on this development, and here we set the stage by introducing complex numbers and explaining some of their natural links with rotations of the plane. There is a lot of information in this lecture, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further. In particular the last slide (page 9) could easily be stared at for an hour or two.
Even old hands at complex analysis may find something novel here to stimulate their thinking, as I insist on a completely logical and rational approach to mathematics--no waffling with angles or ``transcendental notions/functions'' involving ``real numbers''. In fact such a pure algebraic approach is exactly what is needed to set the stage for a good understanding of quaternions.
In particular you will learn that the most fundamental fact about complex numbers is properly stated using the notion of quadrance, that turns are a viable substitute for angles, and that the rational parametrization of a circle is intimately linked to a quadratic map at the level of complex numbers. These ideas will prepare us for appreciating the rotation problem in three dimensions, which we tackle in the next lecture, and then the introduction of quaternions, which we explain in the following one.
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist?
list=PL8403C2F0C89B1333
Year 9 Maths: https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
Ancient Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
Wild West Banking: https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
Sociology and Pure Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: https://www.youtube.com/playlist?list=PL55C7C83781CF4316
Wild Trig: Intro to Rational Trigonometry: https://www.youtube.com/playlist?list=PL3C58498718451C47
MathFoundations: https://www.youtube.com/playlist?list=PL5A714C94D40392AB
Wild Linear Algebra: https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
Famous Math Problems: https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
Probability and Statistics: An Introduction: https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
Boole's Logic and Circuit Analysis: https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
Universal Hyperbolic Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
Differential Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
Algebraic Topology: https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8
Math Seminars: https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
Six: An elementary course in pure mathematics: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
Algebraic Calculus One: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
Algebraic Calculus Two: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
м
- published: 17 May 2013
- views: 117722
41:09
Quaternions are Amazing and so is William Rowan Hamilton!
Quaternions are amazing, they made modern vector mathematics. But how were they created and how do they work? In order to explain all that I am providing both a...
Quaternions are amazing, they made modern vector mathematics. But how were they created and how do they work? In order to explain all that I am providing both a fun biography of Hamilton AND a biography of quaternions and the couplets that led to them.
My website: http://www.KathyLovesPhysics.com
My book "The Lightning Tamers" on Amazon: https://amzn.to/3I7N4mq
Patreon: https://www.patreon.com/user?u=15291200
AudioBook Go Fund Me: https://www.gofundme.com/f/donate-to-help-me-make-an-audiobook?utm_campaign=p_lico+share-sheet&utm_medium=copy_link&utm_source=customer
Anne van Weerden's Website:
https://annevanweerden.nl/Entrance.html
"A Victorian Marriage"
https://annevanweerden.nl/VictorianMarriage.html#Publications
Full song of "William Rowan Hamilton": https://youtu.be/SZXHoWwBcDc
Cover art uses (with permission) the amazing sand sculpture by Daniel Doyle.
I highly recommend glancing at his blog about it, just beautiful!
https://steemit.com/art/@ammonite/i-j-k-ijk-1-sand-sculpture
0:00 Why I made this video
2:08 Hamilton's Career (History)
6:46 Couple/Couplet Theory (Math)
10:28 Hamilton's Personal Life (History)
15:34 Quaternions (Math)
31:55 Hamilton's Legacy (History)
39:20 What's Next
https://wn.com/Quaternions_Are_Amazing_And_So_Is_William_Rowan_Hamilton
Quaternions are amazing, they made modern vector mathematics. But how were they created and how do they work? In order to explain all that I am providing both a fun biography of Hamilton AND a biography of quaternions and the couplets that led to them.
My website: http://www.KathyLovesPhysics.com
My book "The Lightning Tamers" on Amazon: https://amzn.to/3I7N4mq
Patreon: https://www.patreon.com/user?u=15291200
AudioBook Go Fund Me: https://www.gofundme.com/f/donate-to-help-me-make-an-audiobook?utm_campaign=p_lico+share-sheet&utm_medium=copy_link&utm_source=customer
Anne van Weerden's Website:
https://annevanweerden.nl/Entrance.html
"A Victorian Marriage"
https://annevanweerden.nl/VictorianMarriage.html#Publications
Full song of "William Rowan Hamilton": https://youtu.be/SZXHoWwBcDc
Cover art uses (with permission) the amazing sand sculpture by Daniel Doyle.
I highly recommend glancing at his blog about it, just beautiful!
https://steemit.com/art/@ammonite/i-j-k-ijk-1-sand-sculpture
0:00 Why I made this video
2:08 Hamilton's Career (History)
6:46 Couple/Couplet Theory (Math)
10:28 Hamilton's Personal Life (History)
15:34 Quaternions (Math)
31:55 Hamilton's Legacy (History)
39:20 What's Next
- published: 31 Jan 2023
- views: 134075
1:01
Land Rover Discovery | Project Discovery with Laird Hamilton
Land Rover Ambassador and big-wave surfing pioneer Laird Hamilton is no stranger to displaying resilience in the face of one of nature’s most powerful forces. A...
Land Rover Ambassador and big-wave surfing pioneer Laird Hamilton is no stranger to displaying resilience in the face of one of nature’s most powerful forces. After a year of unprecedented challenge Laird mirrors Land Rover’s Project Discovery and examines the source of resilience itself. Find out more: https://bit.ly/3D4J56e
https://wn.com/Land_Rover_Discovery_|_Project_Discovery_With_Laird_Hamilton
Land Rover Ambassador and big-wave surfing pioneer Laird Hamilton is no stranger to displaying resilience in the face of one of nature’s most powerful forces. After a year of unprecedented challenge Laird mirrors Land Rover’s Project Discovery and examines the source of resilience itself. Find out more: https://bit.ly/3D4J56e
- published: 02 Oct 2021
- views: 83717
56:14
The rotation problem and Hamilton's discovery of quaternions III | Famous Math Problems 13c
This is the third lecture on the problem of how to extend the algebraic structure of the complex numbers to deal with rotations in space, and Hamilton's discove...
This is the third lecture on the problem of how to extend the algebraic structure of the complex numbers to deal with rotations in space, and Hamilton's discovery of quaternions, and here we roll up the sleaves and get to work laying out a concise but logically clear framework for this remarkable structure.
A main tool that we will use is the algebra of 2x2 matrices, however with (rational) complex number entries. This allows us a simplified way of proving the various laws of arithmetic for quaternions, and brings ideas from linear algebra, like the determinant and the trace of a matrix, into play.
We end with an important visual model of quaternions and the key formula that connects them with rotations of three dimensional space. There is a lot in this lecture, so be prepared to go slowly, take it in bite size pieces if necessary, and try your hand at the problems!
In the next and final lecture on this topic, we will amplify our understanding of the rotation mapping, and show how quaternions can be practically used to realize rotations and their compositions. All without any use of transcendental notions such as angle, cos or sin-- a big step forward in the conceptual understanding of this subject!!
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist?
list=PL8403C2F0C89B1333
Year 9 Maths: https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
Ancient Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
Wild West Banking: https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
Sociology and Pure Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: https://www.youtube.com/playlist?list=PL55C7C83781CF4316
Wild Trig: Intro to Rational Trigonometry: https://www.youtube.com/playlist?list=PL3C58498718451C47
MathFoundations: https://www.youtube.com/playlist?list=PL5A714C94D40392AB
Wild Linear Algebra: https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
Famous Math Problems: https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
Probability and Statistics: An Introduction: https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
Boole's Logic and Circuit Analysis: https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
Universal Hyperbolic Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
Differential Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
Algebraic Topology: https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8
Math Seminars: https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
Six: An elementary course in pure mathematics: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
Algebraic Calculus One: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
Algebraic Calculus Two: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
м
https://wn.com/The_Rotation_Problem_And_Hamilton's_Discovery_Of_Quaternions_Iii_|_Famous_Math_Problems_13C
This is the third lecture on the problem of how to extend the algebraic structure of the complex numbers to deal with rotations in space, and Hamilton's discovery of quaternions, and here we roll up the sleaves and get to work laying out a concise but logically clear framework for this remarkable structure.
A main tool that we will use is the algebra of 2x2 matrices, however with (rational) complex number entries. This allows us a simplified way of proving the various laws of arithmetic for quaternions, and brings ideas from linear algebra, like the determinant and the trace of a matrix, into play.
We end with an important visual model of quaternions and the key formula that connects them with rotations of three dimensional space. There is a lot in this lecture, so be prepared to go slowly, take it in bite size pieces if necessary, and try your hand at the problems!
In the next and final lecture on this topic, we will amplify our understanding of the rotation mapping, and show how quaternions can be practically used to realize rotations and their compositions. All without any use of transcendental notions such as angle, cos or sin-- a big step forward in the conceptual understanding of this subject!!
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist?
list=PL8403C2F0C89B1333
Year 9 Maths: https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
Ancient Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
Wild West Banking: https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
Sociology and Pure Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: https://www.youtube.com/playlist?list=PL55C7C83781CF4316
Wild Trig: Intro to Rational Trigonometry: https://www.youtube.com/playlist?list=PL3C58498718451C47
MathFoundations: https://www.youtube.com/playlist?list=PL5A714C94D40392AB
Wild Linear Algebra: https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
Famous Math Problems: https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
Probability and Statistics: An Introduction: https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
Boole's Logic and Circuit Analysis: https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
Universal Hyperbolic Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
Differential Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
Algebraic Topology: https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8
Math Seminars: https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
Six: An elementary course in pure mathematics: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
Algebraic Calculus One: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
Algebraic Calculus Two: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
м
- published: 24 Jul 2013
- views: 27356
59:46
The rotation problem and Hamilton's discovery of quaternions (II) | Famous Math Problems 13b
This is the second of three lectures on Hamilton's discovery of quaternions, and here we introduce rotations of three dimensional space and the natural problem ...
This is the second of three lectures on Hamilton's discovery of quaternions, and here we introduce rotations of three dimensional space and the natural problem of how to describe them effectively and compose them. We discuss the geometry of the sphere, take a detour to talk about composing planar rotations with different centers, talk about the connections between reflections and rotations, and introduce the basic algebraic framework with vectors, the dot product and the cross product. As in the first lecture, there is a lot of information here, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further.
Euler's theorem on the composition of rotations is an important ingredient. You will also learn that a curious addition of spherical vectors on the surface of a sphere provides an effective visual calculus for composing rotations.
This lecture prepares us for the next, where we introduce Hamilton's quaternions, which connect the dot product and cross product in a remarkable way, and yield probably the most effective current technique for managing rotations in graphics, video games and rocket science. So yes, this is really rocket science!
Video Contents:
00:00 Introduction to rotations and their composition-
03:25 Rotations of 3-Dimensional space ( geometrically )
09:38 Planar situation
14:25 Algebra of planar rotations
23:36 Rotation of 3D space as a product of 2 reflections
37:04 Algebra of 3D Rotations about 0
42:57 Euler theorem - The product of two rotations is a rotation
44:40 The analytic approach ( via Linear Algebra)
48:24 How to define 2 directions to be perpendicular; vectors
52:43 Cross product of 2 vectors
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist?
list=PL8403C2F0C89B1333
Year 9 Maths: https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
Ancient Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
Wild West Banking: https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
Sociology and Pure Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: https://www.youtube.com/playlist?list=PL55C7C83781CF4316
Wild Trig: Intro to Rational Trigonometry: https://www.youtube.com/playlist?list=PL3C58498718451C47
MathFoundations: https://www.youtube.com/playlist?list=PL5A714C94D40392AB
Wild Linear Algebra: https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
Famous Math Problems: https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
Probability and Statistics: An Introduction: https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
Boole's Logic and Circuit Analysis: https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
Universal Hyperbolic Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
Differential Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
Algebraic Topology: https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8
Math Seminars: https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
Six: An elementary course in pure mathematics: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
Algebraic Calculus One: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
Algebraic Calculus Two: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
м
https://wn.com/The_Rotation_Problem_And_Hamilton's_Discovery_Of_Quaternions_(Ii)_|_Famous_Math_Problems_13B
This is the second of three lectures on Hamilton's discovery of quaternions, and here we introduce rotations of three dimensional space and the natural problem of how to describe them effectively and compose them. We discuss the geometry of the sphere, take a detour to talk about composing planar rotations with different centers, talk about the connections between reflections and rotations, and introduce the basic algebraic framework with vectors, the dot product and the cross product. As in the first lecture, there is a lot of information here, so by all means take it slowly, and break it up by pausing and absorbing the ideas before going further.
Euler's theorem on the composition of rotations is an important ingredient. You will also learn that a curious addition of spherical vectors on the surface of a sphere provides an effective visual calculus for composing rotations.
This lecture prepares us for the next, where we introduce Hamilton's quaternions, which connect the dot product and cross product in a remarkable way, and yield probably the most effective current technique for managing rotations in graphics, video games and rocket science. So yes, this is really rocket science!
Video Contents:
00:00 Introduction to rotations and their composition-
03:25 Rotations of 3-Dimensional space ( geometrically )
09:38 Planar situation
14:25 Algebra of planar rotations
23:36 Rotation of 3D space as a product of 2 reflections
37:04 Algebra of 3D Rotations about 0
42:57 Euler theorem - The product of two rotations is a rotation
44:40 The analytic approach ( via Linear Algebra)
48:24 How to define 2 directions to be perpendicular; vectors
52:43 Cross product of 2 vectors
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist?
list=PL8403C2F0C89B1333
Year 9 Maths: https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
Ancient Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
Wild West Banking: https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
Sociology and Pure Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: https://www.youtube.com/playlist?list=PL55C7C83781CF4316
Wild Trig: Intro to Rational Trigonometry: https://www.youtube.com/playlist?list=PL3C58498718451C47
MathFoundations: https://www.youtube.com/playlist?list=PL5A714C94D40392AB
Wild Linear Algebra: https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
Famous Math Problems: https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
Probability and Statistics: An Introduction: https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
Boole's Logic and Circuit Analysis: https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
Universal Hyperbolic Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
Differential Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
Algebraic Topology: https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8
Math Seminars: https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
Six: An elementary course in pure mathematics: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
Algebraic Calculus One: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
Algebraic Calculus Two: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
м
- published: 01 May 2013
- views: 46288
1:01:32
The rotation problem and Hamilton's discovery of quaternions IV | Famous Math Problems 13d
We show how to practically implement the use of quaternions to describe the algebra of rotations of three dimensional space. The key idea is to use the notion o...
We show how to practically implement the use of quaternions to describe the algebra of rotations of three dimensional space. The key idea is to use the notion of half-turn [or half-slope--I have changed terminology since this video was made!] instead of angle: this is well suited to connect with the lovely algebraic structure of quaternions.
The theory of half turns is interesting in its own right, and belongs to what we call Vector Trigonometry--an interesting variant of Rational Trigonometry that we intend to describe in detail elsewhere. Here we only need a few formulas for half turns, which really go back to the ancient Greeks and the rational parametrization of the unit circle which we have discussed many times!
By focussing on the formula for quaternion multiplication in terms of scalar and vector parts, we can deduce that any orthonormal set of vectors u,v and w act algebraically just like the familiar unit vectors l,j and k. That allows us to decompose the multiplication of a general quaternion into its action on two perpendicular planes: this is the key to understanding the geometry of quaternion multiplication.
It allows us to easily see the effect of multiplying on the left by q and on the right be the conjugate. After a normalization by the quadrance of q, we get a rotation of the vector part of the space, which is the connection with rotations that we seek.
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist?
list=PL8403C2F0C89B1333
Year 9 Maths: https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
Ancient Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
Wild West Banking: https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
Sociology and Pure Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: https://www.youtube.com/playlist?list=PL55C7C83781CF4316
Wild Trig: Intro to Rational Trigonometry: https://www.youtube.com/playlist?list=PL3C58498718451C47
MathFoundations: https://www.youtube.com/playlist?list=PL5A714C94D40392AB
Wild Linear Algebra: https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
Famous Math Problems: https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
Probability and Statistics: An Introduction: https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
Boole's Logic and Circuit Analysis: https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
Universal Hyperbolic Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
Differential Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
Algebraic Topology: https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8
Math Seminars: https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
Six: An elementary course in pure mathematics: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
Algebraic Calculus One: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
Algebraic Calculus Two: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
м
https://wn.com/The_Rotation_Problem_And_Hamilton's_Discovery_Of_Quaternions_Iv_|_Famous_Math_Problems_13D
We show how to practically implement the use of quaternions to describe the algebra of rotations of three dimensional space. The key idea is to use the notion of half-turn [or half-slope--I have changed terminology since this video was made!] instead of angle: this is well suited to connect with the lovely algebraic structure of quaternions.
The theory of half turns is interesting in its own right, and belongs to what we call Vector Trigonometry--an interesting variant of Rational Trigonometry that we intend to describe in detail elsewhere. Here we only need a few formulas for half turns, which really go back to the ancient Greeks and the rational parametrization of the unit circle which we have discussed many times!
By focussing on the formula for quaternion multiplication in terms of scalar and vector parts, we can deduce that any orthonormal set of vectors u,v and w act algebraically just like the familiar unit vectors l,j and k. That allows us to decompose the multiplication of a general quaternion into its action on two perpendicular planes: this is the key to understanding the geometry of quaternion multiplication.
It allows us to easily see the effect of multiplying on the left by q and on the right be the conjugate. After a normalization by the quadrance of q, we get a rotation of the vector part of the space, which is the connection with rotations that we seek.
************************
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger
My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things.
Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/algebraic-calculus-one/ Please join us for an exciting new approach to one of mathematics' most important subjects!
If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at https://www.patreon.com/njwildberger Your support would be much appreciated.
***********************
Here are all the Insights into Mathematics Playlists:
Elementary Mathematics (K-6) Explained: https://www.youtube.com/playlist?
list=PL8403C2F0C89B1333
Year 9 Maths: https://www.youtube.com/playlist?list=PLIljB45xT85CcGpZpO542YLPeDIf1jqXK
Ancient Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85Aqe2b4FBWUGJdYROT6-o4e
Wild West Banking: https://www.youtube.com/playlist?list=PLIljB45xT85DB7CzoFWvA920NES3g8tJH
Sociology and Pure Mathematics: https://www.youtube.com/playlist?list=PLIljB45xT85A-qCypcmZqRvaS1pGXpTua
Old Babylonian Mathematics (with Daniel Mansfield): https://www.youtube.com/playlist?
list=PLIljB45xT85CdeBmQZ2QiCEnPQn5KQ6ov
Math History: https://www.youtube.com/playlist?list=PL55C7C83781CF4316
Wild Trig: Intro to Rational Trigonometry: https://www.youtube.com/playlist?list=PL3C58498718451C47
MathFoundations: https://www.youtube.com/playlist?list=PL5A714C94D40392AB
Wild Linear Algebra: https://www.youtube.com/playlist?list=PLIljB45xT85BhzJ-oWNug1YtUjfWp1qAp
Famous Math Problems: https://www.youtube.com/playlist?list=PLIljB45xT85Bfc-S4WHvTIM7E-ir3nAOf
Probability and Statistics: An Introduction: https://www.youtube.com/playlist?list=PLIljB45xT85AMigTyprOuf__daeklnLse
Boole's Logic and Circuit Analysis: https://www.youtube.com/playlist?list=PLIljB45xT85CnIGIWb7tH1F_S2PyOC8rb
Universal Hyperbolic Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85CN9oJ4gYkuSQQhAtpIucuI
Differential Geometry: https://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP
Algebraic Topology: https://www.youtube.com/playlist?list=PL6763F57A61FE6FE8
Math Seminars: https://www.youtube.com/playlist?list=PLBF39AFBBC3FB30AF
************************
And here are the Wild Egg Maths Playlists:
Triangle Centres: https://www.youtube.com/watch?v=iLBGXDSUohM&list=PLzdiPTrEWyz6VcJQ5xcuqY6g4DWjvpmjM
Six: An elementary course in pure mathematics: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4KD007Ge10dfrDVc4YwlYS
Algebraic Calculus One: https://www.youtube.com/playlist?list=PLzdiPTrEWyz4rKFN541wFKvKPSg5Ea6XB
Algebraic Calculus Two: https://www.youtube.com/playlist?list=PLzdiPTrEWyz5VLVr-0LPPgm4T1mtU_DG-
м
- published: 09 Aug 2013
- views: 27205
1:05:29
Discovery Conference 2023 Hamilton Morris and Robin Carhart Harris
Discovery Conference is The Bay Area's annual Psychedelics conference at The Midway in San Francisco. Get more information at www.discoverycon-sf.org.
Discovery Conference is The Bay Area's annual Psychedelics conference at The Midway in San Francisco. Get more information at www.discoverycon-sf.org.
https://wn.com/Discovery_Conference_2023_Hamilton_Morris_And_Robin_Carhart_Harris
Discovery Conference is The Bay Area's annual Psychedelics conference at The Midway in San Francisco. Get more information at www.discoverycon-sf.org.
- published: 16 May 2023
- views: 1485
1:54
Did Hamilton Somerville's Wife Commit His Murder?
Hamilton Summerville dies of a toxic drug overdose. His family believes that his wife, Donna, is motivated by greed and money as she’ll inherit everything.
Fo...
Hamilton Summerville dies of a toxic drug overdose. His family believes that his wife, Donna, is motivated by greed and money as she’ll inherit everything.
For more go to http://www.investigationdiscovery.com/tv-shows/vanity-fair-confidential/
Vanity Fair Confidential
MONDAY 9/8C
#VanityFairConfidential
Subscribe to Investigation Discovery | https://www.youtube.com/user/DiscoveryID
http://www.investigationdiscovery.com -
---
True Crime Files by Investigation Discovery
Add Hundreds of Crime Shows to Amazon Prime - Start Your 7-Day Free Trial Today!
http://investigationdiscovery.com/TrueCrimeFiles
https://wn.com/Did_Hamilton_Somerville's_Wife_Commit_His_Murder
Hamilton Summerville dies of a toxic drug overdose. His family believes that his wife, Donna, is motivated by greed and money as she’ll inherit everything.
For more go to http://www.investigationdiscovery.com/tv-shows/vanity-fair-confidential/
Vanity Fair Confidential
MONDAY 9/8C
#VanityFairConfidential
Subscribe to Investigation Discovery | https://www.youtube.com/user/DiscoveryID
http://www.investigationdiscovery.com -
---
True Crime Files by Investigation Discovery
Add Hundreds of Crime Shows to Amazon Prime - Start Your 7-Day Free Trial Today!
http://investigationdiscovery.com/TrueCrimeFiles
- published: 25 Mar 2016
- views: 23659
4:33
AWURADE YE LIVE By DIANA HAMILTON At Trinity Baptist Church Ghana || PL Crew ||
I want to thank you all for your continuous support. This is only the beginning!!! MUCH LOVE❤️
LIKE, SHARE & SUBSCRIBE to my channel
Let’s become friends
Inst...
I want to thank you all for your continuous support. This is only the beginning!!! MUCH LOVE❤️
LIKE, SHARE & SUBSCRIBE to my channel
Let’s become friends
Instagram - https://www.instagram.com/its_nyb/
Facebook - https://web.facebook.com/NyB-927723850688902/
Snapchat - nyb70
#dianahamilton #jesus #music #viral #ghana #drums #youtubeshorts #youtube #party #praise #church #musician #energy #dance #vibes #groove #drumming #subscribe #share #explore #discovery #musiclife #trending #vlog #joemettle #trends #bandlife #world #inspiration #motivation #passion #explorepage #fyp #concerts #band #family #afrobeat #dianahamiltonsongs
https://wn.com/Awurade_Ye_Live_By_Diana_Hamilton_At_Trinity_Baptist_Church_Ghana_||_Pl_Crew_||
I want to thank you all for your continuous support. This is only the beginning!!! MUCH LOVE❤️
LIKE, SHARE & SUBSCRIBE to my channel
Let’s become friends
Instagram - https://www.instagram.com/its_nyb/
Facebook - https://web.facebook.com/NyB-927723850688902/
Snapchat - nyb70
#dianahamilton #jesus #music #viral #ghana #drums #youtubeshorts #youtube #party #praise #church #musician #energy #dance #vibes #groove #drumming #subscribe #share #explore #discovery #musiclife #trending #vlog #joemettle #trends #bandlife #world #inspiration #motivation #passion #explorepage #fyp #concerts #band #family #afrobeat #dianahamiltonsongs
- published: 25 Feb 2024
- views: 68
1:01
Project Discovery | Laird Hamilton
Big-wave surfing pioneer Laird Hamilton is no stranger to displaying resilience in the face of one of nature’s most powerful forces. After a year of unprecedent...
Big-wave surfing pioneer Laird Hamilton is no stranger to displaying resilience in the face of one of nature’s most powerful forces. After a year of unprecedented challenge Laird examines the source of resilience itself and looks forward to new adventures.
Learn more about the Discovery: https://landroverau.click/discoYT
https://wn.com/Project_Discovery_|_Laird_Hamilton
Big-wave surfing pioneer Laird Hamilton is no stranger to displaying resilience in the face of one of nature’s most powerful forces. After a year of unprecedented challenge Laird examines the source of resilience itself and looks forward to new adventures.
Learn more about the Discovery: https://landroverau.click/discoYT
- published: 11 Oct 2021
- views: 13290
9:56
23-Year-Old Mystery Solved: The Shocking Discovery of William Dashawn Hamilton's Murder
This video revolves around the 23-year-old mystery of William Dashawn Hamilton's murder, which was recently solved. The video starts by emphasizing the signific...
This video revolves around the 23-year-old mystery of William Dashawn Hamilton's murder, which was recently solved. The video starts by emphasizing the significance of the truth and how it can never be concealed, no matter how long it takes. It further explains how criminals often think they can get away with their crimes, but the truth will eventually catch up with them. The host welcomes the viewers to AF Crime and urges them to like, subscribe, and turn on notifications to stay updated on future uploads.
The video then moves on to the story of a young reporter named Angeline who, in 1999, was called by the police chief of DeKalb County in Georgia to investigate the discovery of a child's remains in a nearby cemetery. Upon reaching the site, Angeline was horrified to find the remains of a young child who had been dead for 3-6 months. The investigating team found that the dead child was an African-American boy, but despite releasing his description to the press, they could not find his relatives.
The host goes on to explain how Angeline made it her mission to find the identity of the child and locate his relatives. She even advocated for the child on America's Most Wanted and continued to do so even after she joined The National Center for Missing & Exploited Children as a media director. However, the mystery was finally solved last year when a popular artist who was an AI technology maestro provided a digitally drawn picture of the young child that resembled the 6-year-old child at the time of his death.
The video explains that with the help of the portrait and other evidence found, an anonymous tipper named Ava came forward and revealed the identity of the child as William Dashawn Hamilton. Ava further revealed that William came from Charlotte in the company of his mother, Teresa Ann Bailey Black, who was later convicted of his murder. The video ends by emphasizing the importance of the truth and how it always has a way of revealing itself, no matter how long it takes.
https://wn.com/23_Year_Old_Mystery_Solved_The_Shocking_Discovery_Of_William_Dashawn_Hamilton's_Murder
This video revolves around the 23-year-old mystery of William Dashawn Hamilton's murder, which was recently solved. The video starts by emphasizing the significance of the truth and how it can never be concealed, no matter how long it takes. It further explains how criminals often think they can get away with their crimes, but the truth will eventually catch up with them. The host welcomes the viewers to AF Crime and urges them to like, subscribe, and turn on notifications to stay updated on future uploads.
The video then moves on to the story of a young reporter named Angeline who, in 1999, was called by the police chief of DeKalb County in Georgia to investigate the discovery of a child's remains in a nearby cemetery. Upon reaching the site, Angeline was horrified to find the remains of a young child who had been dead for 3-6 months. The investigating team found that the dead child was an African-American boy, but despite releasing his description to the press, they could not find his relatives.
The host goes on to explain how Angeline made it her mission to find the identity of the child and locate his relatives. She even advocated for the child on America's Most Wanted and continued to do so even after she joined The National Center for Missing & Exploited Children as a media director. However, the mystery was finally solved last year when a popular artist who was an AI technology maestro provided a digitally drawn picture of the young child that resembled the 6-year-old child at the time of his death.
The video explains that with the help of the portrait and other evidence found, an anonymous tipper named Ava came forward and revealed the identity of the child as William Dashawn Hamilton. Ava further revealed that William came from Charlotte in the company of his mother, Teresa Ann Bailey Black, who was later convicted of his murder. The video ends by emphasizing the importance of the truth and how it always has a way of revealing itself, no matter how long it takes.
- published: 20 Mar 2023
- views: 236
9:29
Kaitlin Hamilton - Discovery Talks
The Ohio State University's Kaitlin Hamilton delivers her Discovery Talk 'Mitochondria and Macrophages: New Directions in Cystic Fibrosis Research.' Presented b...
The Ohio State University's Kaitlin Hamilton delivers her Discovery Talk 'Mitochondria and Macrophages: New Directions in Cystic Fibrosis Research.' Presented by Infectious Diseases, a focus area of Ohio State's Discovery Themes.
https://wn.com/Kaitlin_Hamilton_Discovery_Talks
The Ohio State University's Kaitlin Hamilton delivers her Discovery Talk 'Mitochondria and Macrophages: New Directions in Cystic Fibrosis Research.' Presented by Infectious Diseases, a focus area of Ohio State's Discovery Themes.
- published: 20 Feb 2018
- views: 74
3:03
The World's Most Potent Psychedelic | HAMILTON'S PHARMACOPEIA
The Bufo Alvarius toad can have its venom glands milked for the powerful psychedelic 5-MeO-DMT. But conservationists have warned that could threaten the surviva...
The Bufo Alvarius toad can have its venom glands milked for the powerful psychedelic 5-MeO-DMT. But conservationists have warned that could threaten the survival of the species.
Watch more from VICE TV:
Hamilton Morris Spews After Taking Peyote
https://www.youtube.com/watch?v=nTr3dW0RRlM
How Not to Cook Meth
https://www.youtube.com/watch?v=FtTZ-CZ_a4Q
Using the Psychedelic Iboga to Treat Addiction
https://www.youtube.com/watch?v=YEL71eGc6DQ
#VICETVArchive
Subscribe Now: https://vice.video/SUBSCRIBE-TO-VICETV
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VICETV.com | https://www.vicetv.com
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Newsletter | http://bit.ly/1kpnyN6
https://wn.com/The_World's_Most_Potent_Psychedelic_|_Hamilton'S_Pharmacopeia
The Bufo Alvarius toad can have its venom glands milked for the powerful psychedelic 5-MeO-DMT. But conservationists have warned that could threaten the survival of the species.
Watch more from VICE TV:
Hamilton Morris Spews After Taking Peyote
https://www.youtube.com/watch?v=nTr3dW0RRlM
How Not to Cook Meth
https://www.youtube.com/watch?v=FtTZ-CZ_a4Q
Using the Psychedelic Iboga to Treat Addiction
https://www.youtube.com/watch?v=YEL71eGc6DQ
#VICETVArchive
Subscribe Now: https://vice.video/SUBSCRIBE-TO-VICETV
Follow VICE TV:
VICETV.com | https://www.vicetv.com
VICE Video | https://video.vice.com
Facebook | https://www.facebook.com/vicetv
Twitter | https://twitter.com/vicetv
Instagram | http://instagram.com/vicetv
Newsletter | http://bit.ly/1kpnyN6
- published: 06 Dec 2022
- views: 178543
2:02
Amazing Dinosaur Discovery | Hamilton NZ | 2020
Amazing Dinosaur Discovery | Hamilton NZ | 2020
https://youtu.be/6gwqj9wimz4
Subscribe to Our Youtube Channel – JNS Videos
https://www.youtube.com/c/jnsvide...
Amazing Dinosaur Discovery | Hamilton NZ | 2020
https://youtu.be/6gwqj9wimz4
Subscribe to Our Youtube Channel – JNS Videos
https://www.youtube.com/c/jnsvideos
Like Our Facebook Page
JNS Videos : https://www.facebook.com/videos77777/
Amazing Dinosaur Discovery, JNS Videos, Dinosaur Kids, Dinosaur, Hamilton, New Zealand, Te Rapa, Pukete
#AmazingDinosaurDiscovery #JNSVideos #DinosaurKids #Dinosaur #Hamilton #NewZealand #TeRapa #Pukete
https://wn.com/Amazing_Dinosaur_Discovery_|_Hamilton_Nz_|_2020
Amazing Dinosaur Discovery | Hamilton NZ | 2020
https://youtu.be/6gwqj9wimz4
Subscribe to Our Youtube Channel – JNS Videos
https://www.youtube.com/c/jnsvideos
Like Our Facebook Page
JNS Videos : https://www.facebook.com/videos77777/
Amazing Dinosaur Discovery, JNS Videos, Dinosaur Kids, Dinosaur, Hamilton, New Zealand, Te Rapa, Pukete
#AmazingDinosaurDiscovery #JNSVideos #DinosaurKids #Dinosaur #Hamilton #NewZealand #TeRapa #Pukete
- published: 23 Jan 2020
- views: 1394
1:01
Land Rover Project Discovery | Laird Hamilton
Surfpionier Laird Hamilton staat er om bekend dat hij is opgewassen tegen de enorme natuurkrachten van de oceaan. Na een jaar van beperkende omstandigheden geef...
Surfpionier Laird Hamilton staat er om bekend dat hij is opgewassen tegen de enorme natuurkrachten van de oceaan. Na een jaar van beperkende omstandigheden geeft Laird zijn visie op Land Rover's #ProjectDiscovery en evalueert hij waar het bij menselijke veerkracht om gaat.
Meer Discovery: https://bit.ly/3ahQQti
Beleef Land Rover online:
Website: http://www.landrover.nl
Facebook: https://www.facebook.com/landrover
Twitter: https://twitter.com/landrover
Instagram: https://www.instagram.com/landrover
https://wn.com/Land_Rover_Project_Discovery_|_Laird_Hamilton
Surfpionier Laird Hamilton staat er om bekend dat hij is opgewassen tegen de enorme natuurkrachten van de oceaan. Na een jaar van beperkende omstandigheden geeft Laird zijn visie op Land Rover's #ProjectDiscovery en evalueert hij waar het bij menselijke veerkracht om gaat.
Meer Discovery: https://bit.ly/3ahQQti
Beleef Land Rover online:
Website: http://www.landrover.nl
Facebook: https://www.facebook.com/landrover
Twitter: https://twitter.com/landrover
Instagram: https://www.instagram.com/landrover
- published: 10 Oct 2021
- views: 1032
2:26
Connect to Hamilton - OCE Discovery
We partnered with the entire #HamOnt innovation ecosystem at this year's Ontario Centres of Excellence Discovery event!
Event-goers connected to Hamilton as we...
We partnered with the entire #HamOnt innovation ecosystem at this year's Ontario Centres of Excellence Discovery event!
Event-goers connected to Hamilton as we brought together McMaster University & Mohawk College, Innovation Factory & The Forge - Hamilton, Hamilton Economic Development, and partners from across this city.
We were joined by innovative Hamilton start ups like Nix Sensor Ltd., Lumago Inc., Brüha, OverAir, Cinnos, 180 Drums, Nuts For Cheese, Aiva Labs and so many more. What an amazing opportunity to connect our city and bring the entire ecosystem together!
Check out the video here:
https://wn.com/Connect_To_Hamilton_Oce_Discovery
We partnered with the entire #HamOnt innovation ecosystem at this year's Ontario Centres of Excellence Discovery event!
Event-goers connected to Hamilton as we brought together McMaster University & Mohawk College, Innovation Factory & The Forge - Hamilton, Hamilton Economic Development, and partners from across this city.
We were joined by innovative Hamilton start ups like Nix Sensor Ltd., Lumago Inc., Brüha, OverAir, Cinnos, 180 Drums, Nuts For Cheese, Aiva Labs and so many more. What an amazing opportunity to connect our city and bring the entire ecosystem together!
Check out the video here:
- published: 25 May 2017
- views: 76
6:48
Tripping on the World's Oldest Psychedelic | HAMILTON'S PHARMACOPEIA
In Season 3 of HAMILTON'S PHARMACOPEIA, Hamilton journeys to South America on a quest to understand the legend of Bufotenine – the world's oldest psychedelic.
...
In Season 3 of HAMILTON'S PHARMACOPEIA, Hamilton journeys to South America on a quest to understand the legend of Bufotenine – the world's oldest psychedelic.
Watch more like this:
Hamilton Morris Meets Meth Addicts Hooked on God
https://www.youtube.com/watch?v=fJDGJgB_AKI
The Toad Venom Pamphlet That Changed Psychedelia Forever
https://www.youtube.com/watch?v=3WMA1_PdgRQ
Tripping on Hallucinogenic Frogs
https://www.youtube.com/watch?v=C3Yd7M3JNlw
Subscribe Now: https://vice.video/SUBSCRIBE-TO-VICETV
Follow VICE TV:
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Newsletter | http://bit.ly/1kpnyN6
https://wn.com/Tripping_On_The_World's_Oldest_Psychedelic_|_Hamilton'S_Pharmacopeia
In Season 3 of HAMILTON'S PHARMACOPEIA, Hamilton journeys to South America on a quest to understand the legend of Bufotenine – the world's oldest psychedelic.
Watch more like this:
Hamilton Morris Meets Meth Addicts Hooked on God
https://www.youtube.com/watch?v=fJDGJgB_AKI
The Toad Venom Pamphlet That Changed Psychedelia Forever
https://www.youtube.com/watch?v=3WMA1_PdgRQ
Tripping on Hallucinogenic Frogs
https://www.youtube.com/watch?v=C3Yd7M3JNlw
Subscribe Now: https://vice.video/SUBSCRIBE-TO-VICETV
Follow VICE TV:
VICETV.com | https://www.vicetv.com
VICE Video | https://video.vice.com
Facebook | https://www.facebook.com/vicetv
Twitter | https://twitter.com/vicetv
Instagram | http://instagram.com/vicetv
Newsletter | http://bit.ly/1kpnyN6
- published: 21 Dec 2021
- views: 6068749
8:28
The Toad Venom Pamphlet That Changed Psychedelia Forever | HAMILTON'S PHARMACOPEIA
Haunted by his past mistakes, Hamilton embarks on a journey to correct an error in his reporting while identifying the origin of an international toad venom smo...
Haunted by his past mistakes, Hamilton embarks on a journey to correct an error in his reporting while identifying the origin of an international toad venom smoking phenomenon.
In Season 3 of HAMILTON'S PHARMACOPEIA, Hamilton continues his odyssey into the historical, chemical and societal impacts of some of the world's most unique drugs. He learns more about LSD, bufotenine, 5-MeO-DMT, DMT and more.
Watch more like this:
The Fish That Gets You High
https://youtu.be/6N3j5g066CU
Hamilton Meets with a Cacti Expert
https://youtu.be/jgADsY_vWkI
Hamilton Morris Meets with Folk Healers of Thailand
https://youtu.be/p-dXRqYU7-Y
Subscribe Now: https://vice.video/SUBSCRIBE-TO-VICETV
Follow VICE TV:
VICETV.com | https://www.vicetv.com
VICE Video | https://video.vice.com
Facebook | https://www.facebook.com/vicetv
Twitter | https://twitter.com/vicetv
Instagram | http://instagram.com/vicetv
Newsletter | http://bit.ly/1kpnyN6
https://wn.com/The_Toad_Venom_Pamphlet_That_Changed_Psychedelia_Forever_|_Hamilton'S_Pharmacopeia
Haunted by his past mistakes, Hamilton embarks on a journey to correct an error in his reporting while identifying the origin of an international toad venom smoking phenomenon.
In Season 3 of HAMILTON'S PHARMACOPEIA, Hamilton continues his odyssey into the historical, chemical and societal impacts of some of the world's most unique drugs. He learns more about LSD, bufotenine, 5-MeO-DMT, DMT and more.
Watch more like this:
The Fish That Gets You High
https://youtu.be/6N3j5g066CU
Hamilton Meets with a Cacti Expert
https://youtu.be/jgADsY_vWkI
Hamilton Morris Meets with Folk Healers of Thailand
https://youtu.be/p-dXRqYU7-Y
Subscribe Now: https://vice.video/SUBSCRIBE-TO-VICETV
Follow VICE TV:
VICETV.com | https://www.vicetv.com
VICE Video | https://video.vice.com
Facebook | https://www.facebook.com/vicetv
Twitter | https://twitter.com/vicetv
Instagram | http://instagram.com/vicetv
Newsletter | http://bit.ly/1kpnyN6
- published: 07 Dec 2021
- views: 1358969
1:43
Hamilton County Discovery Workshop Invitation
@jpmcdon John McDonald invites you to be a part of the upcoming Discovery Workshop in Hamilton County.
@jpmcdon John McDonald invites you to be a part of the upcoming Discovery Workshop in Hamilton County.
https://wn.com/Hamilton_County_Discovery_Workshop_Invitation
@jpmcdon John McDonald invites you to be a part of the upcoming Discovery Workshop in Hamilton County.
- published: 21 Dec 2023
- views: 63
3:21
Digital Discovery Gala 2020 - Hamilton Chapter
ProAction Cops & Kids is building trust and relationships between cops, kids and communities. Prepare to be inspired!
Learn more: https://www.copsandkids.ca/
ProAction Cops & Kids is building trust and relationships between cops, kids and communities. Prepare to be inspired!
Learn more: https://www.copsandkids.ca/
https://wn.com/Digital_Discovery_Gala_2020_Hamilton_Chapter
ProAction Cops & Kids is building trust and relationships between cops, kids and communities. Prepare to be inspired!
Learn more: https://www.copsandkids.ca/
- published: 14 May 2021
- views: 9
13:02
Delicious Discovery: Shanghai Restaurant SkyCity Hamilton Food Review | First-Timer's Impressions!"
Join me on my Yum Cha journey as I venture into the delightful world of Shanghai Restaurant at SkyCity Hamilton for my very first food review! From mouthwateri...
Join me on my Yum Cha journey as I venture into the delightful world of Shanghai Restaurant at SkyCity Hamilton for my very first food review! From mouthwatering dishes to the ambiance, I share my honest thoughts and impressions. If you're a foodie or planning to visit SkyCity Hamilton, this review is a must-watch for a taste of what awaits you at Shanghai Restaurant. Don't forget to like, comment, and subscribe for more exciting food adventures! 🍜🌆 #FoodReview #ShanghaiRestaurant #SkyCityHamilton #FirstTimeEater
https://wn.com/Delicious_Discovery_Shanghai_Restaurant_Skycity_Hamilton_Food_Review_|_First_Timer's_Impressions
Join me on my Yum Cha journey as I venture into the delightful world of Shanghai Restaurant at SkyCity Hamilton for my very first food review! From mouthwatering dishes to the ambiance, I share my honest thoughts and impressions. If you're a foodie or planning to visit SkyCity Hamilton, this review is a must-watch for a taste of what awaits you at Shanghai Restaurant. Don't forget to like, comment, and subscribe for more exciting food adventures! 🍜🌆 #FoodReview #ShanghaiRestaurant #SkyCityHamilton #FirstTimeEater
- published: 09 Dec 2023
- views: 57