JWKennington

Identity in physics can be challenging to find. We’re given a narrow set of labels to choose from, typically theorist or experimentalist, and these can often be time-dependent as we progress in our careers. Throughout my time in the discipline, I’ve worked in experimental labs, theory groups, and more applied settings. Many times I’ve branded myself a theorist, perhaps more out of desire than measure; however, I’ve always wanted a more nuanced way of describing my work, myself, and developmental stage. Short answer: like most things we do, it depends on a clever choice of coordinates. Three different classification systems (two 2D and one 1D) gathered from leading theorists, compiled. Measures features like preference for mathematical or intuitive tools, goals of analyzing existing models or constructing new ones, reliance on rigor, sophistication of computational tools, etc. See full post for more, including XKCD-style visuals (because why not):

Recently had to reconcile multiple keys for similar git hosts, and found several posts that were nearly sufficient. Summarized the method that worked for me in terms of namespacing the ssh credentials, hope it’s useful if you find yourself in the same position!

Often in discussions about blackholes, the question arises of observer experience when falling into a blackhole. Due to the extreme tidal forces experienced along such a path, the observer would be stretched out - a process colloquially referred to as spaghettification. This week I would like to look at a happier use for spaghetti near blackholes. If an observer in a stable circular orbit around the supermassive blackhole at the center of our galaxy were to use spaghetti as a tether, how much spaghetti would be required? Restated, the Fermi-Problem question of interest this week is:

> How much spaghetti would be required to form the smallest stable circle around the supermassive blackhole at the center of the Milky Way?

Without giving away the numerical answer, the result is around 3 meals for everyone on Earth!

I first encountered a diagram of algebraic structures at the end of Jeevanjee's second chapter, "Vector Spaces", which elegantly summarizes the high-level differences in structure between sets, vector spaces, and inner product spaces. I've attempted to augment this map along two dimensions: a structure dimension that aims to measure the number of attributes an algebraic object has, and a specificity dimension that measures the number of constraints placed on each attribute.

This is aimed primarily at mathematical physics, and is intended as a quick reference -- it's obviously incomplete and isn't a substitute for Hungerford, Lang, or [insert favorite algebra book].

I hope you find it as helpful as I did in making it!

I first encountered a diagram of algebraic structures at the end of Jeevanjee's second chapter, "Vector Spaces", which elegantly summarizes the high-level differences in structure between sets, vector spaces, and inner product spaces.

I've attempted to augment this map along two dimensions: a structure dimension that aims to measure the number of attributes an algebraic object has, and a specificity dimension that measures the number of constraints placed on each attribute.

This is aimed primarily at mathematical physics, and is intended as a quick reference -- it's obviously incomplete and isn't a substitute for Hungerford, Lang, or [insert favorite algebra book].

I hope you find it as helpful as I did in making it!

I've cleaned up the last paragraph, and replaced my friend's reasoning with the term "momentum" to avoid confusion. thanks for feedback

It was weird - I've reparaphrased that to be "momentum" now for improved clarity. thanks for feedback

Photons have momentum. momentum is analogous to mass in special relativity (specifically, mass is the 0 component of the four-momentum)

Hence I said my friend was being a bit “interpretive”. He really meant that though photons have zero rest mass, they nonzero inertial mass (E=mc^2)

I wrote a blog post describing the tensor product in terms of functional programming techniques in python https://jwkennington.com/blog/tensor-product-for-programmers...

I would also be interested in a "math for programmers" approach to deciphering formalism. I've studied a fair amount of linear algebra / differential geometry and could see how Python-definitions might help. I'm less familiar with other areas of mathematics

But how am I supposed to know that AB is one mathematical object here instead of the 2 separate objects A, B? My point is that there should be a graphical way other than "put them arbitrarily close" to link them together

I prefer your second notation, with the tensor product happening in parenthesis, but it kind of defeats the point of the graphical nature of the notation if we need to explictly write the tensor product I think..

Slight nit-pick, but matrix multiplication is not exclusively a contraction, but rather a contraction on the tensor product of the two matrices. See the next paragraph for why this is concerning.

I find this notation great for simple applications, but potentially unwieldy for dim > 2. For instance, how would I represent the tensor (or outer) product of two matrices? the inputs would be two circles with two lines attached to each, the result would need to be a single circle with four lines attached. The natural attempt would be something like:

  a    - o -
      /    /
     |    /
     \   |
  ab  ---o---
         |   \
        /    |
       /    /
  b    - o -

But I suspect the above diagram isn't correct because there are no "open" indices at the end of this. Rather, this diagram seems to represent the contraction of a 4D tensor with 2, 2D tensors.

It seems we we would need a way of connecting circles without implying a contraction of a particular index.

Anyone know how to annotate the outer product of two matrices in this diagrammatic convention?

It’s exactly what it says on the can - a list of my favorite texts. You can get the books anywhere, not sure what you’re angry about.

I’m in the process of reviewing each in depth, but haven’t gotten to many yet, though I do own all of them. I will post the individual reviews (the “content” I’m assuming you’re expecting, though I didn’t say was there), so stay tuned for those. Appreciate your feedback

Good point - I’ll repost without the “show”. I figured that it was a list of texts, each of which can be “tried out”, but if - as you suggest - the criterion really only applies to code, then I’ll change the post

Update: removed the “show” from the title - thanks for the policing (I don’t want to use hacker news improperly, I love this site)

I too am enamored with Hagoromo; however, I wasn't able to get any of the Japanese chalk. I have been using the South Korean produced Hagoromo and find it quite nice. How do you think the Japanese vs. South Korean produced chalks compare?

Good note about the microfiber! I'll have to try that. I've become increasingly frustrated with erasers. When it comes to washing the board, do you use a squeegee at all? I've found a sponge/squeegee combo to make cleaning quick.

A dimension of chalk usage that seems to be missing from your page - what do you think of chucks (holders)? Hagoromo chalk is quite wide (11mm) and it seems that most chalk holders are built for 9mm chalk. I use the Hagoromo branch chalk holders, they seem to have good grip. The other alternative I've found is to look for artist-oriented graphite or pastel holders.

I had to explain tensor products to several of my developer friends and realized that they found the rigorous approach somewhat obstructive. When I recast the subject in terms of functional programming (specifically, the pattern of currying), the group seemed to understand better.

Tensors are a "hot topic" in modern computing (AI, tensorflow, etc.), but it's surprising how many practicing computer scientists (or data scientists) think of tensors as "n-dimensional arrays" instead of "multilinear maps". Most of the modern mathematical theory emphasizes the latter viewpoint, though some texts (such as Goodfellow's Deep Learning) land in the middle. Goodfellow does adopt an unusual convention for Einstein summation, but that's a subject for a different post...

Thanks for reading. Let me know if there is anything in the post I might clarify!

I wanted to provide a different answer from many of those "glad I left" answers here. I sympathize with those "keep the physics brain alive" goals of other commenters.

Physics undergrad (2015) with thesis in nonlinear dynamics, but have done research in astro. Always wanted to do GR-related research.

Landed an awesome job in quantitative finance where I write computational code (distributed computation) for various purposes (researching markets, analyzing risk, etc.). Job is interesting - but not "capital I" Interesting in the same way that physics was. I guess that is part of the trade-off.

I'm considering going back to academia - especially in light of the G-wave phenomena finally having sizeable datasets to analyse in recent years - its getting increasingly difficult to keep my studies of physics/math at "hobby" level.

Interested to hear if anyone else out there has "gone back".