He must have realized that apart from tech bros, there is not a single person in the world that likes him including his father and his step mother who also happens to be his step sister.

I hope by AI they don’t mean LLMs because that is not the correct architecture for this job but definitely what every crook would go for to get funds.

That gives me a good idea. A week before the protest buy burners, use them frequently near republican supporters’ house, go to a protest, use your phone all the time in the protest, dump them near the police, let them enjoy the fruits of the regime they supported.

and cover your face if you are in a shithole country like USA, Turkey, Russia etc

If solid torus yes, if just the regular torus (surface of the solid torus) no. CD is homotopic to a circle and so is a solid torus.

Even if it has thickness still homotopic to a circle. For instance a band with thickness is homotopic to a circle, you can retract along the radius to arrive at a circle that is inside the band. Similarly a plane, or a slab with thickness are all homotopic to a point.

Note that all of these are proved by using collections of transformations from the space to itself (not necessarily from the space to all of itself though, if it maps the space to a subset of it that is fine). So if you want to say something like “but you can also shrink a circle to eventually reach a point but it is not homotopic to a point” that won’t work because you are imagining transformation that maps a circle not into itself but to a smaller one.

ps: the actual definition of homotopy equivalence between “objects” is slightly more involved but intuitively it boils down to this when you imagine one space as a subset of the other and try to see if they are homotopy equivalent.

well so much hype has been generated around chatgpt being close to AGI that now it makes sense to ask questions like “can chatgpt prove the Riemann hypothesis”

they always seem to go together for some reason

that bird is doing its best and is very proud of its achievements, leave it alone OK?

a torus is not homotopic to a straw though unless you take the straw and glue it at its ends. a straw is homotopic to a circle, a torus is homotopic to product of two circles, Baldur’s gate is homotopic to a disk which is homotopic to a point unless we are talking about the game storage medium which used to be a CD which is also homotopic to a circle