• FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I

    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
  • Possible cave discovery ,May 2016 .Hamilton Ontario Canada .

    published: 13 May 2016
  • All-New Land Rover Discovery – Surfing with Laird Hamilton

    The All-New Land Rover Discovery receives the surfing seal of approval as legendary surfer Laird Hamilton and 8-year old surfing prodigy Jett Prefontaine take the ultimate family SUV on a surf adventure in Malibu. In a display of incredible versatility, smart technology and capability, the All-New Discovery proves why it’s the perfect SUV for any adventure. Visit http://bit.ly/2fBmbtf for more All-New Discovery Information.

    published: 15 Nov 2016
  • FamousMathProbs13b: The rotation problem and Hamilton's discovery of quaternions (II)

    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
  • FamousMathProbs13d: The rotation problem and Hamilton's discovery of quaternions IV

    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 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 vecto...

    published: 09 Aug 2013
  • Hamilton Discovery School

    Hamilton Discovery School Talent Show

    published: 19 May 2017
  • 2016 Discovery Days in Health Sciences Hamilton

    Our 4th annual Discovery Day in Health Sciences hosted by Hamilton Health Sciences gave area high school students and teachers another opportunity to explore careers in medicine and other sciences via a keynote lecture, hands-on workshops and an interactive lab demo which concluded the day. Take a peak at some of the things we did and share the excitement!

    published: 31 Aug 2016
  • FamousMathProbs13c: The rotation problem and Hamilton's discovery of quaternions III

    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
  • Mark Hamilton - The Neothink Society 2012 World Summit

    Mark Hamilton addresses the hundreds of Neothink Society World Summit 2012 attendees with an update of the new Twelve Visions Party (TVP) platform and his latest literature, "The Prime Cure"

    published: 24 Aug 2012
  • Hamilton, Boole and their Algebras - Professor Raymond Flood

    Professor Flood gives a fabulous overvierw of the lives and work of two mathematicians, Hamilton and Boole: http://www.gresham.ac.uk/lectures-and-events/hamilton-boole-and-their-algebras William Rowan Hamilton (1805-1865) revolutionized algebra with his discovery of quaternions, a non-commutative algebraic system, as well as his earlier work on complex numbers. George Boole (1815-1864) contributed to probability and differential equations, but his greatest achievement was to create an algebra of logic 'Boolean algebra'. These new algebras were not only important to the development of algebra but remain of current use. The transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and-events/hamilton-boole-and-their-...

    published: 01 Dec 2015
  • 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
  • Forbes Hamilton, Land Rover Discovery

    Forbes regularly takes his Land Rover Discovery on 4x4 adventures in the wilds of the west of Scotland, we join him for a fun journey and ask him what else is important in his life. See more at http://crazyway.tv

    published: 17 May 2016
  • Tyler Hamilton - The true price of winning at all costs

    The Discovery Vitality Summit, held from 15-17 August this year, featured a number of keynote speakers, both local and international. One of the main draw cards was Tyler Hamilton, former professional cyclist and teammate of Lance Armstrong. In his talk, Tyler opened up about his journey and the choices he made that led him to become a cycling champion and a user of doping substances. He also fielded questions from the audience about his experience. The footage is an edited version of his talk.

    published: 18 Sep 2013
  • Una de las sectas mas crueles "The family"( Anne Hamilton Byrne)

    SI ASI LO DESEAS PUEDES AGREGARME EN FACEBOOK : https://www.facebook.com/joe.psych.5 el 30 de noviembre pasado , crearon un documental , acerca de una de las sectas mas crueles de los años 60s , la cual se autodominaba "the family " ,a continuación te hablare acerca de ella...

    published: 07 Dec 2016
  • Metamorphosis- Ayahuasca Documentary

    Ayahuasca has been used by Shamans and those they help for hundreds if not thousands of years. Found all over the Amazon, Ayahuasca and it's incredible ability to heal has been slowly but steadily creeping into western consciousness. Metamorphosis is a documentary that follows several westerners as they undergo five Ayahuasca ceremonies and experience the gamut of emotions - from utter fear to outright ecstasy. It also explores the shamans who work with the medicine as well as all the key elements of an Ayahuasca ceremony. The film also tells the story of Hamilton Souther, who earlier in life had no belief of and in spirit. After having a spiritual awakening, Hamilton is led to the Amazon where he apprentices as an Ayahuascero, or person who practices medicine with Ayahuasca. Hamilton and ...

    published: 15 Aug 2014
  • Surfing With 2017 Land Rover Discovery and Laird Hamilton

    Surf legend Laird Hamilton and eight-year old phenomenon Jett Prefontaine take New Discovery surfing at Point Mugu in Malibu, California ahead of its U.S. premiere Hamilton demonstrates Intelligent Seat Fold technology by rearranging premium SUV’s seats from the water(3) Intelligent Seat Fold technology allows customers to reconfigure the second and third row seats remotely using a smartphone(3) Members of the Silicon Beach Surfers club join Laird and Jett to check out the new Land Rover SUV’s surf-friendly features, including the waterproof Activity Key wristband New Discovery Dynamic Design Pack receives debut at LA Auto Show New Discovery can accommodate seven surfers in comfort If you like DPCcars videos please subscribe: https://goo.gl/BSIaFc

    published: 15 Nov 2016
FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I

FamousMathProbs 13a: The rotation problem and Hamilton's discovery of quaternions I

  • Order:
  • Duration: 58:24
  • Updated: 17 May 2013
  • views: 56933
videos
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 each lecture. Great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
https://wn.com/Famousmathprobs_13A_The_Rotation_Problem_And_Hamilton's_Discovery_Of_Quaternions_I
Possible cave discovery ,May 2016 .Hamilton Ontario Canada .

Possible cave discovery ,May 2016 .Hamilton Ontario Canada .

  • Order:
  • Duration: 5:55
  • Updated: 13 May 2016
  • views: 591
videos
https://wn.com/Possible_Cave_Discovery_,May_2016_.Hamilton_Ontario_Canada_.
All-New Land Rover Discovery – Surfing with Laird Hamilton

All-New Land Rover Discovery – Surfing with Laird Hamilton

  • Order:
  • Duration: 1:45
  • Updated: 15 Nov 2016
  • views: 26894
videos
The All-New Land Rover Discovery receives the surfing seal of approval as legendary surfer Laird Hamilton and 8-year old surfing prodigy Jett Prefontaine take the ultimate family SUV on a surf adventure in Malibu. In a display of incredible versatility, smart technology and capability, the All-New Discovery proves why it’s the perfect SUV for any adventure. Visit http://bit.ly/2fBmbtf for more All-New Discovery Information.
https://wn.com/All_New_Land_Rover_Discovery_–_Surfing_With_Laird_Hamilton
FamousMathProbs13b: The rotation problem and Hamilton's discovery of quaternions (II)

FamousMathProbs13b: The rotation problem and Hamilton's discovery of quaternions (II)

  • Order:
  • Duration: 59:47
  • Updated: 01 May 2013
  • views: 21911
videos
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! Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of each lecture. Great for review, study and summary.
https://wn.com/Famousmathprobs13B_The_Rotation_Problem_And_Hamilton's_Discovery_Of_Quaternions_(Ii)
FamousMathProbs13d: The rotation problem and Hamilton's discovery of quaternions IV

FamousMathProbs13d: The rotation problem and Hamilton's discovery of quaternions IV

  • Order:
  • Duration: 1:01:33
  • Updated: 09 Aug 2013
  • views: 12198
videos
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 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 each lecture. Great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/.... I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?... .
https://wn.com/Famousmathprobs13D_The_Rotation_Problem_And_Hamilton's_Discovery_Of_Quaternions_Iv
Hamilton Discovery School

Hamilton Discovery School

  • Order:
  • Duration: 2:27
  • Updated: 19 May 2017
  • views: 5
videos https://wn.com/Hamilton_Discovery_School
2016 Discovery Days in Health Sciences   Hamilton

2016 Discovery Days in Health Sciences Hamilton

  • Order:
  • Duration: 3:01
  • Updated: 31 Aug 2016
  • views: 301
videos
Our 4th annual Discovery Day in Health Sciences hosted by Hamilton Health Sciences gave area high school students and teachers another opportunity to explore careers in medicine and other sciences via a keynote lecture, hands-on workshops and an interactive lab demo which concluded the day. Take a peak at some of the things we did and share the excitement!
https://wn.com/2016_Discovery_Days_In_Health_Sciences_Hamilton
FamousMathProbs13c: The rotation problem and Hamilton's discovery of quaternions III

FamousMathProbs13c: The rotation problem and Hamilton's discovery of quaternions III

  • Order:
  • Duration: 56:14
  • Updated: 24 Jul 2013
  • views: 12658
videos
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 each lecture. Great for review, study and summary.
https://wn.com/Famousmathprobs13C_The_Rotation_Problem_And_Hamilton's_Discovery_Of_Quaternions_Iii
Mark Hamilton - The Neothink Society 2012 World Summit

Mark Hamilton - The Neothink Society 2012 World Summit

  • Order:
  • Duration: 17:47
  • Updated: 24 Aug 2012
  • views: 44766
videos
Mark Hamilton addresses the hundreds of Neothink Society World Summit 2012 attendees with an update of the new Twelve Visions Party (TVP) platform and his latest literature, "The Prime Cure"
https://wn.com/Mark_Hamilton_The_Neothink_Society_2012_World_Summit
Hamilton, Boole and their Algebras - Professor Raymond Flood

Hamilton, Boole and their Algebras - Professor Raymond Flood

  • Order:
  • Duration: 54:56
  • Updated: 01 Dec 2015
  • views: 4511
videos
Professor Flood gives a fabulous overvierw of the lives and work of two mathematicians, Hamilton and Boole: http://www.gresham.ac.uk/lectures-and-events/hamilton-boole-and-their-algebras William Rowan Hamilton (1805-1865) revolutionized algebra with his discovery of quaternions, a non-commutative algebraic system, as well as his earlier work on complex numbers. George Boole (1815-1864) contributed to probability and differential equations, but his greatest achievement was to create an algebra of logic 'Boolean algebra'. These new algebras were not only important to the development of algebra but remain of current use. The transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and-events/hamilton-boole-and-their-algebras Gresham College has been giving free public lectures since 1597. This tradition continues today with all of our five or so public lectures a week being made available for free download from our website. There are currently over 1,800 lectures free to access or download from the website. Website: http://www.gresham.ac.uk Twitter: http://twitter.com/GreshamCollege Facebook: https://www.facebook.com/greshamcollege Instagram: http://www.instagram.com/greshamcollege
https://wn.com/Hamilton,_Boole_And_Their_Algebras_Professor_Raymond_Flood
Connect to Hamilton - OCE Discovery

Connect to Hamilton - OCE Discovery

  • Order:
  • Duration: 2:26
  • Updated: 25 May 2017
  • views: 56
videos
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
Forbes Hamilton, Land Rover Discovery

Forbes Hamilton, Land Rover Discovery

  • Order:
  • Duration: 4:47
  • Updated: 17 May 2016
  • views: 9
videos
Forbes regularly takes his Land Rover Discovery on 4x4 adventures in the wilds of the west of Scotland, we join him for a fun journey and ask him what else is important in his life. See more at http://crazyway.tv
https://wn.com/Forbes_Hamilton,_Land_Rover_Discovery
Tyler Hamilton - The true price of winning at all costs

Tyler Hamilton - The true price of winning at all costs

  • Order:
  • Duration: 26:34
  • Updated: 18 Sep 2013
  • views: 59990
videos
The Discovery Vitality Summit, held from 15-17 August this year, featured a number of keynote speakers, both local and international. One of the main draw cards was Tyler Hamilton, former professional cyclist and teammate of Lance Armstrong. In his talk, Tyler opened up about his journey and the choices he made that led him to become a cycling champion and a user of doping substances. He also fielded questions from the audience about his experience. The footage is an edited version of his talk.
https://wn.com/Tyler_Hamilton_The_True_Price_Of_Winning_At_All_Costs
Una de las sectas mas crueles  "The family"( Anne Hamilton Byrne)

Una de las sectas mas crueles "The family"( Anne Hamilton Byrne)

  • Order:
  • Duration: 3:58
  • Updated: 07 Dec 2016
  • views: 18403
videos
SI ASI LO DESEAS PUEDES AGREGARME EN FACEBOOK : https://www.facebook.com/joe.psych.5 el 30 de noviembre pasado , crearon un documental , acerca de una de las sectas mas crueles de los años 60s , la cual se autodominaba "the family " ,a continuación te hablare acerca de ella...
https://wn.com/Una_De_Las_Sectas_Mas_Crueles_The_Family_(_Anne_Hamilton_Byrne)
Metamorphosis- Ayahuasca Documentary

Metamorphosis- Ayahuasca Documentary

  • Order:
  • Duration: 1:35:35
  • Updated: 15 Aug 2014
  • views: 810878
videos
Ayahuasca has been used by Shamans and those they help for hundreds if not thousands of years. Found all over the Amazon, Ayahuasca and it's incredible ability to heal has been slowly but steadily creeping into western consciousness. Metamorphosis is a documentary that follows several westerners as they undergo five Ayahuasca ceremonies and experience the gamut of emotions - from utter fear to outright ecstasy. It also explores the shamans who work with the medicine as well as all the key elements of an Ayahuasca ceremony. The film also tells the story of Hamilton Souther, who earlier in life had no belief of and in spirit. After having a spiritual awakening, Hamilton is led to the Amazon where he apprentices as an Ayahuascero, or person who practices medicine with Ayahuasca. Hamilton and Maestro Don Alberto (an indigenous master shaman for over thirty years that practices with Hamilton) take us through the ceremonies as well as explain the meaning behind them.
https://wn.com/Metamorphosis_Ayahuasca_Documentary
Surfing With 2017 Land Rover Discovery and Laird Hamilton

Surfing With 2017 Land Rover Discovery and Laird Hamilton

  • Order:
  • Duration: 1:52
  • Updated: 15 Nov 2016
  • views: 786
videos
Surf legend Laird Hamilton and eight-year old phenomenon Jett Prefontaine take New Discovery surfing at Point Mugu in Malibu, California ahead of its U.S. premiere Hamilton demonstrates Intelligent Seat Fold technology by rearranging premium SUV’s seats from the water(3) Intelligent Seat Fold technology allows customers to reconfigure the second and third row seats remotely using a smartphone(3) Members of the Silicon Beach Surfers club join Laird and Jett to check out the new Land Rover SUV’s surf-friendly features, including the waterproof Activity Key wristband New Discovery Dynamic Design Pack receives debut at LA Auto Show New Discovery can accommodate seven surfers in comfort If you like DPCcars videos please subscribe: https://goo.gl/BSIaFc
https://wn.com/Surfing_With_2017_Land_Rover_Discovery_And_Laird_Hamilton
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