Mitchell Ostrow

This doesn't say anything about how the attractors is instantiated, ie the equation itself (let alone its mapping to the biology, which is another criterion needed for a mechanism according to Craver). I'm fine with this claim if it's what the post means!

Perhaps what is meant by 'attractors aren't mechanisms' is that you can write down a large number of equations that are attractors (e.g. any diffeomorphism phi that transforms the system dxdt = -x while preserving its asymptotic behavior, also known as a conjugacy).

I should clarify—in my example the system is the linear dynamical equation. When you say system, what are you referring to?

I guess I’m still not following, especially wrt usage of the words caused, composition and organization. Maybe we can use an example? Take dxdt=-x. the dynamics in this system is the decay to the attractor. So I’m not clear how to distinguish the two…

I don't completely follow the second claim--it seems to me that there's no clear hierarchy between a system's behavior and the system, they are one and the same. So why aren't your two statements equivalent? Or are you talking about data--trajectories, and downstream inferences from it--attractors?

among other things relevant to arguing for ring attractor-ness, just thought that was most relevant to your article.

Curious why you didn't include Chaudhuri et al. (2019)? They show that flows from perturbations off the ring manifold are biased back onto the ring (your section on 'Missing Activities')

So no hotdog bowls? (I tried to find the Detroiters clip but couldn't someone pls link)

😀

Hauntingly similar to Slaughterhouse Five: "Billy Pilgrim became unstuck in time"

Shoutout @leokoz8.bsky.social for the amazing visualizer

TLDR;
1. Teach dynamical systems hand in hand with neuroscience (yes, from day one)
2. Don't be scared of the math, but pretty pictures are always nice :)
3. Stick to elegant examples for teaching.
Happy to keep talking about this later / offline!

Here are a few computational neuroscience / biophysics courses (one by my advisor), that use some of these examples (syllabi certainly outdated):
stuff.mit.edu/afs/athena/c...

ocw.mit.edu/courses/8-59...

web.mit.edu/ajemian/www/...

These systems can all be described elegantly (e.g only requiring a handful of equations or order parameters), and illustrate properties of dynamical systems that are fundamentally emergent, i.e they cannot emerge through a 'domino chain'.

Some examples off the top of my head: Hodgkin-Huxley (and reductions, e.g. Fitzhugh-Nagumo), Turing Instability, Synchronization, Predator-Prey systems, Chaos in random RNNs, Ring Attractor / Integrator networks, Hopfield Networks Grid Cell Theory. Someone mentioned Eve Marder earlier and I agree!

So far as teaching in a neuroscientific context goes, it's probably most effective to teach with examples. And the most beautiful examples often come from biophysics / classical theoretical neuroscience:

As a PhD student working on dynamical systems theory applied to neuroscience and ML, nothing beats a good rigorous dynamics curriculum. That being said, one of the reasons I love dynamics is because videos can be so intuitive for understanding complex structures: kozleo.github.io/ds_demo/inde...

Their quote of mine is highly misrepresentative and does not reflect my true stance at all.

where can I get one???