Twitter | Pretraživanje | |
Steve Trettel
Minnesotan. Topology Postdoc . Space nerd, cook, language revitalization activist
262
Tweetovi
1.024
Pratim
620
Osobe koje vas prate
Tweetovi
Steve Trettel 27 min
Odgovor korisniku/ci @nervous_jessica
Wow - beautiful!
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 20 h
Odgovor korisniku/ci @hamish_todd @ZenoRogue
The clips I’ve posted of the earth are also 90deg
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 23 h
Anyone interested in the Nil geometry facts I’ve been tweeting out this week, be sure to check out the work of if you haven’t already 😃
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @roice713
Yeah! For each radius of helix, there’s a sequence of distances along the z axis where they meet back up after one,two,three... rotations. If this were a string these would be the “nodes” of a fixed-frequency vibrational mode. In Nil - they are the conjugate points of the metric!
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @roice713
(These are the coordinates we actually compute the geodesic flow in because the formula is simpler! They are just harder to explain / motivate)
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @roice713
You can change coordinates to a model where the rotation symmetries act like normal rotations of R3. This makes the geodesics look more like actual helices, but the trade off is now the metric tensor looks complicated. Here’s a rendering of some geodesics in these coordinates.
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @roice713
This can be seen in our paper a little if you look at the picture of the balls in nil on pg2. The curves drawn on them are the lines of latitude, which are wiggly precisely because the rotational symmetry acts funny in these coordinates.
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @roice713
It fixes the z-axis, but instead of rotating the orthogonal planes like a rigid rotation of E^3, it actually preserves a collection of hyperbolic paraboloids - like Pringle chips- instead of flat planes.
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @roice713
It’s just an “artifact” of the coordinates which are used. In one since they are the natural ones, because they come from the Heisenberg group and the metric looks simple. But, as a trade off, the extra 1-parameter of “rotations” looks complicated in these coordinates.
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @InertialObservr
Maybe- “the shape of continued fraction approximates of phi” could lead to a nice series of pictures. (Or maybe trash I’m tired af hah)
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @InertialObservr
Fun idea! If you do the “shape of a rational number” this way - it should close up? And the golden ratio is the “least rational” so it’s limit is all over the place. 🤔
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @InertialObservr
Whoa that thing is all over the place!
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @stevejtrettel
Whoops the day got away from me! We will talk about why the earth doesn’t shrink in size as it recedes into the distance (quite unlike what happens in Euclidean space) another day. Here’s a hint 😃
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 6. velj
Odgovor korisniku/ci @InertialObservr
Does the limit of the circles trace out a cool curve?
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 5. velj
Odgovor korisniku/ci @mikeandallie @anniek_p
Thanks! 😀
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 5. velj
Odgovor korisniku/ci @roice713
Haha! Yes Lacan said some pretty crazy things (I had a housemate in graduate school who was reading something in which he mentioned “cybernetic homology” and Klein bottles when talking about the mind). Beautiful animation though!!
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 5. velj
Odgovor korisniku/ci @stevejtrettel
Ok - gotta get through airport security. Will finish the story (4) in a while! Ask away I’ll try and get to your questions while waiting at my gate too :)
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 5. velj
Odgovor korisniku/ci @stevejtrettel
More rings appear as this process repeats: in this figure light reaches the earth along three kinds of paths: headin straight there(green), traversing one large spiral (yellow), or two smaller spirals (blue). This results in a central image surrounded by 1 large and 1 small ring
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 5. velj
Odgovor korisniku/ci @stevejtrettel
As the earth continues to recede, this gap grows - and we see the ring shaped mirage expanding away from the earth with a wider and wider black annulus in between!
Reply Retweet Označi sa "sviđa mi se"
Steve Trettel 5. velj
Odgovor korisniku/ci @stevejtrettel
Looking closely at this, we notice we see the earth in the direction of the red geodesics, and again in the direction of the blue geodesics, but in between we see a thin black circle, of light rays escaping into space!
Reply Retweet Označi sa "sviđa mi se"