Why High-Dimensional Space Is So Strange

Comments · 39

• PR

  @PrairieWindSun · 2 days ago

  When I realized lower n-dimensions were particular versus all the higher dimensions, especially of LLMs with language, it switched my perspective to how special our reality is. Among them is definitely volume mattering so much, sometimes literally.

  5

• DU

  @dukufu · 20 minutes ago

  Replys to the comments are 🔥🔥

• KA

  @KA_POWSKI · 17 hours ago

  The vanishing sphere is how you derive the zero point vector of any sphere.

• CO

  @ConsultantsVC · 3 hours ago

  Very interesting!

• NA

  @Nawskcalbehtmai · 2 days ago

  I wrote the white paper on some of this. True GAI is probabilistic.

  2

• FR

  @frogg03_ · 1 day ago

  What the hell are these comments doing in a technical math video 😭

  2

• BO

  @bonob0123 · 6 hours ago (edited)

  Does that mean the volume of the unit sphere increases up until dimension n = 17 before tending towards zero as an approaches Infinity?<br><br>4/3 is bigger than one so at least in three dimensions the volume increases over the area in two dimensions

  1

• SH

  @sherifffruitfly · 1 day ago

  Yay a gamma function video!

• GS

  @gsestream · 17 hours ago (edited)

  you can think of any dimension space as if similar to 3d space. ie a sphere is just an n-dimensional sphere with same radius. the shape of a sphere is still the same even if adding dimensions. yep you might have fewer samples, but that does not change the shape. you are talking about sampling not the shapes. you can think n-dimensions as being overlapped in 3d space. ie ghost dimensions are just on top of the normal 3d dimensions. transparent. hyperplane is still a flat plane. n-dimensional matrix still can have full rank.

• 이강

  @이강덕-b3m · 2 days ago

  그걸 차원이라고 부르지 말아다오.....

  1

• RA

  @Radoslav-i8c4l · 2 days ago (edited)

  r=? if # 4п r² ≡ #( 4п × r ³÷)÷ⁿ<br>r ≡ ⁿ ≡ (5² - 2²)½

  2

• KA

  @KaliFissure · 1 day ago

  Using a Klein topology the entire CP violation of Quantum mechanics becomes a necessary geometric aspect<br><br><a href="https://www.youtube.com/watch?v=jOsq9vWGydU">https://youtu.be/jOsq9vWGydU?si=nHhozsMcmj0DmM7F</a>