Metachirality!
Hello good humans! Metachirality part 2 is here, pastakitties and all.
There's so much more to say about metachirality and screw symmetry, so many tidbits that didn't make it into the final video... I was thinking of doing a little bonus video that mentions these things, without getting fancy about the narrative so it's quick to make.
Mostly this week is going to be an infrastructure week. I've got a bunch of support stuff to catch up on---paperwork, messages, updating software and shuffling data around, moving and organizing office stuff, learning some new equipment. All the little things that I neglect to do when I'm focusing on pure video-making. I'm hoping I can fit in making the bonus video too, because I'd like to make it but I really want to get back to the Emmy Noether video next week.
Ok the video has finished uploading so I'm gonna end this post now. Thanks for being here and making this work possible. Go forth and find yourself some spirally things around you!
Vi
Comments (29)
Love the video, thank you for that! Would an example of metachirality be the way northern and southern hemisphere toilets and bathtubs drain in reverse-direction whirlpools from each other? For that matter, the way everything rotates in reverse direction between the two hemispheres?
That's a great example of chirality! Not necessarily also metachirality unless the pipes had the water flowing in a spirally way and you wanted to think of the spirally pipe as a section of an infinite spirally spiral. My understanding of laminar flow in pipes is that once the swirly draining gets to the pipe, it goes into a more typical flow pattern due to friction and fluid dynamics, so it can't actually be swirly like a corkscrew. But it sure would be cool if it could :D
your work with chirality reminds me for some reason the work of mc escher, especially his 'angels and devils' theme. edit: short intro here <a href="https://youtu.be/1CYrGpd8k5w" rel="nofollow noopener" target="_blank">https://youtu.be/1CYrGpd8k5w</a>
Angels and Demons is such a wonderful and subtle work! Symmetries of Things specifically talks about the details of this work, and hyperbolic symmetry groups in general, if you're interested :D
<a href="https://en.wikipedia.org/wiki/Caloscypha" rel="nofollow noopener" target="_blank">https://en.wikipedia.org/wiki/Caloscypha</a>
Yes! Thanks for the ID!
Adorable Orange Peel fungi!
On your video you ask for external hard drive suggestions. I've used a seagate 2TB external for 5 yrs w/o fail. It's around ~$65 on Amazon. See <a href="https://amzn.to/2HB28ca" rel="nofollow noopener" target="_blank">https://amzn.to/2HB28ca</a> . Since you are creating so much video, you might consider the seagate 4TB drive ~$99 on Amazon. See <a href="https://amzn.to/2r5Ayg1" rel="nofollow noopener" target="_blank">https://amzn.to/2r5Ayg1</a> . Thanks for all your work. I've followed you for awhile and am a very modest patreon supporter. Mostly because I live a very modest life. BTW, do you have a cat?
Those tool bits, are they for enlarging holes?
You're right that they go in an already-drilled hole! But a hole in what, and what does their chirality have to do with it?
Where do you get your ideas?
Reading copiously, observing the world around me, and listening to others wherever I go, and then once all the things are in my head they collide and get stuck to each other and turn into an idea.
You need to make your own unbent red and white candy canes, where the (standard) left-handed ones are spearmint and the right-handed ones are caraway.
ahahaha what a great teaching tool! I'd buy these.
If you ever decide to revisit this musically, "metachirality" is the same rhythm as "Mr. Duality" (by The Bobs). Great song, consult a youtube near you to hear it.
*consults a youtube* huh. that sure was a song. badoodalydoodaly-yup.
puttin stuff places is what I do best tho
My favourite line was "good kitty". Yes, I'm being super shallow, but somehow the cut and the tone made my day.
The nerd jokes in this one were on a whole other level. 😂
You've done it again. You've created a video that blew my mind! Maybe if I watch it again 3 or 4 times I'll be able to put my mind back together.
"Spirals are in our DNA."? It's been a long winter...
This was a great video (but of course I'd say that; I have "chiral" in my name). One thing I didn't get, though: Are all metachiral objects chiral?
Ooh, good name! All metachiral objects are indeed also chiral. And chiral objects that are normal-chiral, such as all non-screw chiral objects in 3d, can be technically called "orthochiral".
Wait, what *is* the difference between a pastakitty and spring fingers? Surely they both have the same kind of screw symmetry?
Most springs seem to be left-handed, and most noodles right-handed! I bet there's an interesting reason why.
The idea of the infinite screw got me thinking: there are some screws that land you right back where you started in the first place. An airplane can do a loop-de-loop in place (a trivial type of translational symmetry), but it could also trace a loop-de-loop path that spirals to one side, advancing an amount that evenly divides (by N) an orthogonal circle. After N loops, we're back to where we started. What kind of chirality is it that chases its own tail like that? Idempotent screw chirality?
This hints at a pretty rich topic in higher dimensional symmetry and noneuclidean symmetries. In euclidean 3d a spiral that curves instead of going straight forever would lose its screw symmetry (the coils on the inside of the loop are closer together than the coils on the outside), but if space is curved or you loop around into the 4th dimension that's exactly how you can get some very interesting finite metachiral objects, or even parachiral objects (meaning there's more than just a right and left hand version of the symmetry).
Nailed it! Wait, that's not a very chiral comment...
Ahahaha :D