on a company call. my CEO just cited the MIT study saying that 95% of businesses are not seeing any productivity gains from LLMs. his takeaway is that these companies just aren't using it enough or effectively
more likely the latter. the LLMs are proving pretty handy for me personally to come up with quick and dirty solutions to regular solutions and summarising shit. But nothing further really. stuff still takes the same amount of time
Hiiii me is goooood. It's been too long ay! How've you been?
I saw this meme earlier and I had a lot of thoughts about it so here's a lesson you never asked for hehe
i just chucked it in a keep reading in case anyone doesn't want it :)
Honestly, Shaurya my friend is kinda incorrect here. the diagram illustrates (rather incorrectly) projective geometry. After all, it's just a matter of perspective (hope y'all appreciate the pun).
Essentially, the idea revolves around stereographic projection - a question about how points on a real line can be mapped to a circle with it's centre at (0,0.5) and radius 0.5. There is an explicit formula you can use to find the mapping. But for a visual demonstration
You can project (2,0) onto the circle by drawing a line through (0,1) and (2,0) and finding the point of intersection. I'm too lazy to do the maths.
The trouble comes when mapping the points -infinity and infinity. The idea instead is that eventually, if you keep shifting (2,0) further and further to the right, your intersection with the x-axis is eventually at infinity. This naturally wraps around when you have x = -infinity! So (0,1) becomes your "point of infinity". This enables what we call "one point compactification", the entire real number line can be wrapped up into a circle if you include -infinity and infinity as a single point.
Connecting it to the meme, you instead imagine yourself standing at (0,0) looking towards (0,1). where all the yellow lines meet is the point of infinity, the "origin story" for all parallel lines. In this way, we can create an image with depth because the 3 dimensions can be reduced to "2" with the help of some projective geometry! It's something like casting a shadow onto a screen. x
There is also another handy application when it comes to cartography. One of the useful things about this mapping is that you can invert it, so you can go from a point on the circle to a straight line. Thus we can create a stereographic projection of the globe onto a 2D flat surface with this same idea of connecting the "north pole" and some other point to cast a shadow onto the screen.
Most mathematicians do not think like this cos it's super impractical. Except for where it's useful such as computer graphics and graphic design and art. Maths isn't necessary to be good at it, but it helps explain it :D
gamechangershow
ellievsbear
areudirty
pixelskylines
tangentwithtanner
discoholicmusic
titsay
