Math Nerdery with Jason Orendorff and Bina

[JnBrymn]

Once every two years I get a chance to set down with Jason Orendorff and talk about some of the wildest mathematical ideas. To give you an example of what that's like:

• The first time we met we talked about a statistical prison break puzzle that I had come up with and an algorithm for efficiently computing thousands of generations for Conway's Game of Life that Jason had been looking into.
  
• The second time we met, Jason demonstrated a topological proof that you can always circumscribe rectangles into closed curves (this is also the first time that I understood how a Möbius strip is useful in math!). I talked about tying knots in 4 dimensional spheres.

Today was the 3rd time we've met to talk about math and the discussion du jour was 1) my crazy ideas about modeling cognition and 2) Jason's quest to understand "What is a tensor?"

I went first.

It's fairly well accepted that at the neuron level, connections are governed by Hebbian learning – effectively "neurons that fire together wire together". This seems like a sensible explanation for a local phenomenon (how one neuron relates to another), but I'm interested in a higher-level dynamic about global firing pattern of neurons and how they relate to "thoughts". I propose that given the "proper" neural substrate (e.g. proper neuron dynamics, proper connectivity, proper architecture), that Hebbian learning will naturally lead to a higher-order dynamic where "loops'' of stable periodic neuronal firing form. That is, given any particular "familiar" input and system state, the pattern of neuronal firing tends to become self-reinforcing and driven towards a particular chaotic attractor. I would LOVE to learn more about this. Is this idea out there already? As Jason said during the chat, if only I knew the correct terminology to Google maybe I could learn more. Right now I'm, very inaccurately, calling this idea "neural loops". Someone help!

Jason went second.

Jason is on a quest to understand what a tensor is. He's reading The Poor Man's Introduction to Tensors. And in Jason's mind tensors are a central concept in all sorts of "cool ideas" that he likes to think about – for example, tensors come up often in general relativity and in geometric spaces. But he's frustrated that everyone seems to have a different definition of tensor. For example, from college I'm familiar with the Cauchy stress tensor - it's a 3-by-3 matrix that describes the stress situation at any point in a solid. BUT, I have no clue how this relates to the "tensors that are invariant to bases" that the "Poor Man" document talks about. So even though we had an interesting discussion, we are no closer to really just understanding "what is a tensor!?"

I was excited to also have Bina present this morning. She is a student in the Data Science class at Nashville Software School. She loves math and as a 13 year-old tried to understand Riemann’s hypothesis – that's ambitious! I look forward to getting to know Bina as she becomes involved in our community.

Thanks Jason and Bina for your time. Next time let's do this MORE frequently than every 2 years!

[Nathan Brewer]

Hi all, 

Physicist here. I might be able to add to a discussion about tensors especially in the contexts of Quantum Mechanics and General Relativity. I've done plenty with the math over the years and I'd be happy to revisit it, although it has been some time. 

Jason, I think we met at a PyNash lunch and again at the '19 PyNash conference. You gave the THERAC 25 talk, right?

Feel free to reach out,

Nathan (calcumore, brewer....@gmail.com)