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.
![](https://pbs.twimg.com/media/En_UlaAVoAABsDD.jpg)
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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.
![](https://pbs.twimg.com/media/EtFblCnUcAQpqd4.png)
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.)
![](https://pbs.twimg.com/media/EtFcT7PUcAAlgt_.png)
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
![](https://pbs.twimg.com/media/EtFciZ0UYAAwT3Y.png)
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Joe Rogan's podcast is now is listened to 1.5+ billion times per year at around $50-100M/year revenue.
Independent and 100% owned by Joe, no networks, no middle men and a 100M+ people audience.
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https://t.co/RywAiBxA3s
Joe is the #1 / #2 podcast (depends per week) of all podcasts
120 million plays per month source https://t.co/k7L1LfDdcM
https://t.co/aGcYnVDpMu
Independent and 100% owned by Joe, no networks, no middle men and a 100M+ people audience.
👏
https://t.co/RywAiBxA3s
Joe is the #1 / #2 podcast (depends per week) of all podcasts
120 million plays per month source https://t.co/k7L1LfDdcM
![](https://pbs.twimg.com/media/Dv6LSScUYAYVhSM.jpg)
https://t.co/aGcYnVDpMu
![](https://pbs.twimg.com/media/Dv6LrtgVsAE7ZjM.jpg)
Great article from @AsheSchow. I lived thru the 'Satanic Panic' of the 1980's/early 1990's asking myself "Has eveyrbody lost their GODDAMN MINDS?!"
The 3 big things that made the 1980's/early 1990's surreal for me.
1) Satanic Panic - satanism in the day cares ahhhh!
2) "Repressed memory" syndrome
3) Facilitated Communication [FC]
All 3 led to massive abuse.
"Therapists" -and I use the term to describe these quacks loosely - would hypnotize people & convince they they were 'reliving' past memories of Mom & Dad killing babies in Satanic rituals in the basement while they were growing up.
Other 'therapists' would badger kids until they invented stories about watching alligators eat babies dropped into a lake from a hot air balloon. Kids would deny anything happened for hours until the therapist 'broke through' and 'found' the 'truth'.
FC was a movement that started with the claim severely handicapped individuals were able to 'type' legible sentences & communicate if a 'helper' guided their hands over a keyboard.
For three years I have wanted to write an article on moral panics. I have collected anecdotes and similarities between today\u2019s moral panic and those of the past - particularly the Satanic Panic of the 80s.
— Ashe Schow (@AsheSchow) September 29, 2018
This is my finished product: https://t.co/otcM1uuUDk
The 3 big things that made the 1980's/early 1990's surreal for me.
1) Satanic Panic - satanism in the day cares ahhhh!
2) "Repressed memory" syndrome
3) Facilitated Communication [FC]
All 3 led to massive abuse.
"Therapists" -and I use the term to describe these quacks loosely - would hypnotize people & convince they they were 'reliving' past memories of Mom & Dad killing babies in Satanic rituals in the basement while they were growing up.
Other 'therapists' would badger kids until they invented stories about watching alligators eat babies dropped into a lake from a hot air balloon. Kids would deny anything happened for hours until the therapist 'broke through' and 'found' the 'truth'.
FC was a movement that started with the claim severely handicapped individuals were able to 'type' legible sentences & communicate if a 'helper' guided their hands over a keyboard.