The key to teaching division to young students who have only been introduced recently to more complicated mathematics forms is to make the student feel involved with the process, while finding it pleasant at the same time.
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Ok, it's time for a #FUNctionalAnalysis thread! Let's talk about Hilbert spaces. (I hope you like linear algebra, because that's what we're
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
— syzygay (@syzygay1) August 9, 2020
If you want to impress people, you can just say a Hilbert space is just a complete infinite dimensional inner product space and leave it at that, but let's talk about what that actually means.
When you first learn about vectors, you talk about them as arrows in space; things with a magnitude and a direction. These are elements of R^n where n is the number of dimensions of the space you care about.
You also talk about the dot product (or inner product) as a way to tell when vectors are orthogonal. (I'm purposely saying "orthogonal" instead of "perpendicular" here, but when you actually think about arrows, it's the same thing.)
As my linear algebra students are about to see, R^n is far from the only interesting vector space. A classic example is the space of polynomials of dimension less than or equal to n
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The YouTube algorithm that I helped build in 2011 still recommends the flat earth theory by the *hundreds of millions*. This investigation by @RawStory shows some of the real-life consequences of this badly designed AI.
This spring at SxSW, @SusanWojcicki promised "Wikipedia snippets" on debated videos. But they didn't put them on flat earth videos, and instead @YouTube is promoting merchandising such as "NASA lies - Never Trust a Snake". 2/
A few example of flat earth videos that were promoted by YouTube #today:
https://t.co/TumQiX2tlj 3/
https://t.co/uAORIJ5BYX 4/
https://t.co/yOGZ0pLfHG 5/
Flat Earth conference attendees explain how they have been brainwashed by YouTube and Infowarshttps://t.co/gqZwGXPOoc
— Raw Story (@RawStory) November 18, 2018
This spring at SxSW, @SusanWojcicki promised "Wikipedia snippets" on debated videos. But they didn't put them on flat earth videos, and instead @YouTube is promoting merchandising such as "NASA lies - Never Trust a Snake". 2/
A few example of flat earth videos that were promoted by YouTube #today:
https://t.co/TumQiX2tlj 3/
https://t.co/uAORIJ5BYX 4/
https://t.co/yOGZ0pLfHG 5/
The UN just voted to condemn Israel 9 times, and the rest of the world 0.
View the resolutions and voting results here:
The resolution titled "The occupied Syrian Golan," which condemns Israel for "repressive measures" against Syrian citizens in the Golan Heights, was adopted by a vote of 151 - 2 - 14.
Israel and the U.S. voted 'No' https://t.co/HoO7oz0dwr
The resolution titled "Israeli practices affecting the human rights of the Palestinian people..." was adopted by a vote of 153 - 6 - 9.
Australia, Canada, Israel, Marshall Islands, Micronesia, and the U.S. voted 'No' https://t.co/1Ntpi7Vqab
The resolution titled "Israeli settlements in the Occupied Palestinian Territory, including East Jerusalem, and the occupied Syrian Golan" was adopted by a vote of 153 – 5 – 10.
Canada, Israel, Marshall Islands, Micronesia, and the U.S. voted 'No'
https://t.co/REumYgyRuF
The resolution titled "Applicability of the Geneva Convention... to the
Occupied Palestinian Territory..." was adopted by a vote of 154 - 5 - 8.
Canada, Israel, Marshall Islands, Micronesia, and the U.S. voted 'No'
https://t.co/xDAeS9K1kW
View the resolutions and voting results here:
The resolution titled "The occupied Syrian Golan," which condemns Israel for "repressive measures" against Syrian citizens in the Golan Heights, was adopted by a vote of 151 - 2 - 14.
Israel and the U.S. voted 'No' https://t.co/HoO7oz0dwr
The resolution titled "Israeli practices affecting the human rights of the Palestinian people..." was adopted by a vote of 153 - 6 - 9.
Australia, Canada, Israel, Marshall Islands, Micronesia, and the U.S. voted 'No' https://t.co/1Ntpi7Vqab
The resolution titled "Israeli settlements in the Occupied Palestinian Territory, including East Jerusalem, and the occupied Syrian Golan" was adopted by a vote of 153 – 5 – 10.
Canada, Israel, Marshall Islands, Micronesia, and the U.S. voted 'No'
https://t.co/REumYgyRuF
The resolution titled "Applicability of the Geneva Convention... to the
Occupied Palestinian Territory..." was adopted by a vote of 154 - 5 - 8.
Canada, Israel, Marshall Islands, Micronesia, and the U.S. voted 'No'
https://t.co/xDAeS9K1kW